What is module: Definition and 166 Discussions

In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of module generalizes also the notion of abelian group, since the abelian groups are exactly the modules over the ring of integers.
Like a vector space, a module is an additive abelian group, and scalar multiplication is distributive over the operation of addition between elements of the ring or module and is compatible with the ring multiplication.
Modules are very closely related to the representation theory of groups. They are also one of the central notions of commutative algebra and homological algebra, and are used widely in algebraic geometry and algebraic topology.

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  1. A

    Synchronizing module lab volt Model 8110-20

    Hi I am Ken. Nice to meet you. I would like to get some info on this synchronizing module. It has a 3 phase lamp for synchronizing an alternator. Any knows what's the theory behind that flashing lamp? what if the lamp blink very fast or blinking slow? the reason is frequency is out of phase but...
  2. K

    MHB Proving that a module can be decomposed as a direct sum of submodules

    Letting $X$ be a ring and $K$ be an $X$-module, I need to show that **if** $K \cong A \times B$ for some $X$-modules $A,B$, **then** $\exists$ submodules $M'$ and $N'$ of $K$ such that: $K=M' \oplus N'$ $M' \cong A$ $N' \cong B.$----------I understand the concepts of internal and external...
  3. P

    BPSK Fiber Optic Communication technique module.

    Actually out of my personal interest to learn & upgrade my skills I have self volunteered self development of Photonics Simulation software on Python platform. I am basically a software developer. As such I seek some technical information for same related to its development activity. Can you...
  4. F

    Egg drop project landing module

    Homework Statement For my 8th grade honors science class we are currently doing astronomy. We got assigned a project where we have to create a landing module like the module that people land back on Earth in. The catch is that it has to be able to fit in a 10cm x10cm x10cm box and be able to...
  5. M

    Troubleshooting: No Module Named Cython with Ipython Notebook

    Hi guys, I want to use the C-extension of Python (Cython) in order to speed up my Python codes. I have already installed the Cython package using the command $ pip install Cython. Now I want to apply the package in Ipython notebook and when I start with the command: %load_ext cythonmagic I...
  6. Math Amateur

    MHB Noetherian Modules: ACC, Finite Ascending Chain Definition - Bland

    I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Chapter 4, Section 4.2 on Noetherian and Artinian modules and need help with the definition of a noetherian module - in particular I need help with the nature of an ascending chain of submodule ...
  7. caffeinemachine

    MHB Proof Checking: Submodules of a Free Module of Finite Rank over a PID is Also Free of Finite Rank

    I have been trying to prove the following: Let $R$ be a P.I.D. and $M$ be a free module of finite rank over $R$. Then every submodule $N$ of $M$ is a free module with $$\text{rank} N\leq \text{rank} M$$ and here is my "proof": Using the fact that $R$ is a P.I.D., the theorem is trivial...
  8. C

    Realizing 8K x 8 Memory Module: ROM/RAM Addressing

    Question: An 8K x 8 memory module consists of 2K x 8 of ROM which starts from address 1000H and 6K x 8 of RAM which starts from address 2000H. The module is to be realized using 2K x 8 RAM devices and 2K x 8 ROM devices. The RAM devices have active low write enable (WE) and active low chip...
  9. anorlunda

    Modifying My Boat's Keypad Module: Searching for a Heater Pad

    The chartplotter on my boat works fine. But the buttons work via a sealed keypad module. The contacts use (I think) a. Conductive grease. It works fine when the temperatures are 70F (20C) or higher, but not fine when it is colder. I'm fond of that device. I would rather modify it than...
  10. caffeinemachine

    MHB Surjectivity of a Free Module Homomorphism implies injectivity

    I am trying to prove the following:Let $R$ be a commutative ring and $M$ be a free $R$-module having a finite basis of $n$ elements. Let $T:M\to M$ be a surjective $R$-module homomorphism. Then $T$ is injective.Let $I$ be a maximal ideal of $R$. Note that $I$ annihilates $\widehat M:=M/IM$ and...
  11. Math Amateur

    MHB Standard Free Right Module on X

    I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). In Chapter2: Direct Sums and Short Exact Sequences in Section 2.1.16 B&K deal with the standard free right R-module on a set X. I need some help with the meaning of B&K's terminology...
  12. Math Amateur

    MHB Quotient Modules and Module Homomorphisms - Cohn - Corollary 1.16

    I am reading "Introduction to Ring Theory" by P. M. Cohn (Springer Undergraduate Mathematics Series) In Chapter 1: Basics we find Corollary 1.16 on module homomorphisms and quotient modules. I need help with some aspects of the proof. Corollary 1.16 reads as follows: In the above text...
  13. Math Amateur

    MHB Undergraduate Module Theory Books (including rings, of course)

    For those looking for an undergraduate introduction to module theory there is not a great deal of choice regarding textbooks, but two possible texts are as follows: "A First Course in Module Theory" by M.E. Keating of Imperial College, London [Publisher: Imperial College Press, 1998] and...
  14. S

    Fortran Should I use a Fortran module?

    Hello, I want to create one file test.f95 where i can keep all my subroutines and use them whenever i create a new program new.f95. Is the modules the right way to do it?? because when i create a file let's say test.f95 with the module and one other with my main program (new.f95) when i...
  15. PsychonautQQ

    Show that a^2~0 or a^2~1 in Mod 4

    Homework Statement If a I san integer, show that a^2~0 or a^2~1 in mod 4 (~ represent equivalence) Homework Equations The Attempt at a Solution my ATTEMPT: I started with the division algorithm.. a = 2q + 1 for all odd numbers a = 2q + 0 for all even numbers then I squared the...
  16. PsychonautQQ

    What is the significance of the division algorithm in congruent modules?

    Homework Statement ≈ → equivalence "In general, if a is an integer, the division algorithm gives a = qn + r, where 0 ≤ r ≤ n-1 so a≈r (mod n). Thus every residue class module n appears in the list [0], [1]...,[n-1]. In fact, it appears exactly once. I'm having trouble connecting the dots...
  17. Math Amateur

    (Apparently) simple question rearding module homomorphisms

    I am reading Dummit and Foote Chapter 10: Introduction to Module Theory. I am having difficulty seeing exactly why a conclusion to Proposition 27 that D&F claim is "immediate": I hope someone can help. Proposition 27 and its proof read as follows: In the first line of the proof...
  18. Math Amateur

    MHB (Apparently) simple question rearding module homomorphisms

    I am reading Dummit and Foote Chapter 10: Introduction to Module Theory. I am having difficulty seeing exactly why a conclusion to Proposition 27 that D&F claim is "immediate": I hope someone can help. Proposition 27 and its proof read as follows...
  19. J

    SD Card Module Slot Socket Reader to USB - Help please

    Hi I want to use the SD Card Module Slot Socket Reader Module (Link attached) as a micro sd card reader DIRECTLY to my PC. Is it possible to connect to this Module a USB Male connector and use it as a normal sd-card reader? The Module...
  20. D

    Verilog Display Module: Moving Ball & RGB Image Solutions

    Hello, I have to make a Display module in verilog and first time i want to create a ball which is moving and i have a question, the vertial/horizontal synchronization module is done, the question is about displaying the image using RGB. So, i use 640x480 display and 25Mhz clock frequency and...
  21. J

    Help in Heat Trasnfer Module of COMSOL

    Hi i am simulating Heat transfer through bimetal that is builded by SiO2 on one side and Aluminium on other side. But when i apply heat source on one side(Aluminium side)the heat do not get transferred to the other side(SiO2 side) through the interface. Only Aluminium side is showing temperature...
  22. G

    Basis of module and Free module

    We define basis as: Let M be a module over a ring R with unity and let S be a subset of M. Then S is called a basis of M if 1. M is generated by S 2. S is linearly independent set. Also we define free module as An R module M is called a free module if there exists a subset S of M s.t.S...
  23. Tesladude

    How to Create a VGA to Composite Video Converter for RCA Output

    http://m.ebay.com/itm/271230081889?cmd=VIDESC&gxo=true How can I set this module up to have just a single video output so it can work with rca?
  24. M

    Connecting PV Module with Grid

    I am working on a project. I have completed designing PV module in simulink. I have also added MPPT algorithm and Boost Converter. Now I want to connect it with a grid. Can anybody tell me the circuit diagram?
  25. W

    Why Is My Coil Suppressor Circuit Allowing Voltages Above 130V?

    I am trying to make a coil suppressor to restrict any voltage above say 130v. It is a simple VDR RC circuit. I am using a resistance of 47ohm, 250v and a capacitor of .1nF 250v a VDR of 130v. But the circuit is not working as expected. Is it because of the voltage spec of resistance and...
  26. M

    Dynamics Module - Kinematics Problem

    Hi, I have an basic kinematics problem I can't seem to grasp -- hopefully someone can shed some light on it for me? The acceleration, a, of an object is equal to a=s, where s is the distance from the start position. Sketch a graph representing velocity against distance, s, for the...
  27. B

    Module choices as an undergrad

    Hello, I have what I hope is a straightforward question. Simply put, do I need to be careful about the modules I choose to study as a physics undergrad? Some background info to put the question in context; I am a foundation year physics student at my university, upon successful...
  28. S

    MHB Module over a commutative ring

    Hi, Let $A$ be a commutative ring, $M$ an $A-$module and $U,V,V'$ submodules of $M$ such that $U \cap V = U \cap V'$ and $U+V=U+V'$. Does it follow that $V=V'$? The answer is no because the condition that $V \subset V'$ is necessary though I can't find a counterexample. Does someone has a...
  29. M

    Mathematica Mathematica calling module from NDSolve

    Hi, I want to use a module to repeatedly calculate a parameter in NDSolve, but I seem to be having trouble. Here is a simplified version of what I'm doing. In this example, I want to use the difference between v1 and v2 at a given timepoint to calculate the connection between v1 and v2 for...
  30. M

    Fortran [Fortran] subroutines within the same module

    Hi all, I am working on a Fortran 90 program that has many subroutines within the same module. The question is "are all the variables of a called subroutine are available to the calling subroutine without declaring them in the argument list of the called surboutine"? even though they are...
  31. F

    What BIDI SFP plus module Exactly Is?

    As you know, SFP plus transceiver, based on the latest technology, is ideally suited for datacom and storage area network applications. But there are so many SFP plus products, like BIDI SFP plus transceiver. What is BIDI SFP plus module? What is it Exactly used for?
  32. E

    Is there a USB GSM Module with a Development Kit for Sending SMS Alerts?

    USB GSM Module with SDK? I was wondering if anyone knows of a USB GSM Module that comes with some sort of development kit. I would like to develop an application (Probably in C#) and be able to send out SMS/Text messages as alerts to certain events. Most of the GSM Modules I've seen are for...
  33. X

    Pick the easiest module from QM, EM or Relativity.

    The situation is messy so I'll avoid details. I absolutely must do one module this February that is listed as 'level 3' at the Open University without formally taking the prerequisites. I have to teach myself the required mathematics, in two months, to give myself a decent chance of passing. If...
  34. J

    Current Shunt Amplifier Module

    Hello All, I'm designing a test setup that requires the use of a 50A 50mV current shunt to take measurements for a circuit which produces pulsed DC currents up to about 100 kHz or so (highest frequency component anyway). I would like to use this shunt here, but also amplify the signal 10x or...
  35. E

    Understanding Modules: Definition and Properties for Homework

    Homework Statement I am curious if all modules contain 0. Homework Equations A left R-module M over the ring R consists of an abelian group (M, +) and an operation R × M → M such that certain properties hold... The Attempt at a Solution The definition of a module says that it is an...
  36. T

    Creating a ParityBuild Circuit Module

    Homework Statement Create a circuit (a module) called ParityBuild. It takes a parameterized input that is n bits wide. The ParityBuild module then examines the input bit stream and determines the parity (use even parity). The output is a bit stream that is n+1 bits wide, with the parity bit...
  37. H

    What is/how do i measure the module of these bevel gears?

    Hi all, I've got 2 bevel gears that I'm recreating in CAD, I've got the shapes down it's just a little bit of fine tuning with the dimensions, for which I need the module/diametral pitch of the gears. The pinion has 9 teeth and a tip diameter of roughly 39.3mm, and the gear has 14 teeth and a...
  38. marellasunny

    What is a Module? Polynomials & Vector Spaces

    First,could you please clear this doubt- A polynomial with rational coefficients does not form a vector space over the real numbers.So,will this set of polynomials be called a module instead of a vector space? Is my understanding correct?Any thing else I should know about modules? Thanks
  39. D

    NEED HELP reading data from flash memory module

    I am working on trying to get a .bin file from a flash memory module. Am29BL802C I have attached a picture of the chip I am working with, the datasheet, and the pinout of said chip here --> http://forums.hackaday.com/viewtopic.ph ... 994#p10994 I need this file in order to reverse engineer...
  40. A

    [Module theory] Prove that something forms a left R module.

    Homework Statement Suppose that R and S are two rings, M, is a (R-S) bi-module and N is a left R-module. Show that M \otimes N has the structure of a left S-module. The Attempt at a Solution Well, M\otimes N is an Abelian group, so it's enough that I define a scalar product on...
  41. R

    To show a module M = direct sum of Image and kernal of automorphism

    Homework Statement Let R be a unital commutative ring. Let M be an R-module and \varphi : M \rightarrow M a homomorphism. To show: if \varphi \circ \varphi = \varphi then M=ker(\varphi)\oplus im(\varphi) The Attempt at a Solution I have already shown that M=ker(\varphi)\cap im(\varphi)...
  42. L

    Why is my approach for finding the number of R-submodules of E incorrect?

    Homework Statement Let E be an n-dimensional vector space over a field k. Then if R is the ring of diagonal n-by-n matrices over k, E can be considered as a module over R, with the scalar multiplication diag(λ_1,...,λ_n)(a_1*e_1+...+a_n*e_n)=λ_1*a_1*e_1+...+λ_n*a_n*e_n, where e_1..._e_n form...
  43. S

    PV Module Thermal Modeling using Simscape

    Hi, I am working on a project - Thermal Modeling of a PV Module using Simscape (Thermal Blocks). Using convection, conduction and radiation as the basis I wish to calculate heat flow ( and temperature) in different layers of a PV Module. I am very new to Simscape and that is why need help...
  44. Shackleford

    Understanding Left Cosets in Abstract Algebra

    http://i111.photobucket.com/albums/n149/camarolt4z28/untitled.jpg G/N is the set of all left cosets of N in G. I don't understand the notation. a) The permutations are (1,2), (2,3), (3,1). What are the left cosets - <1>, <2>, <3>? That doesn't make sense with permutations. b) I have...
  45. P

    LSAM/Alair Accent module for re-entry

    Just wondering if its possible to reconfugurate an LSAM/Altair accent module to be able to withstand re-entry to earth? What would be used for heat shield upon re-entry?
  46. gluons

    I am stuck with an f90 module with user-defined operations

    I am writing some code which involves numerical integration of a function on a 3D grid of points. I am defining the type vector to refer to these points, and I am also trying to extend the intrinsic operator * to include scalar and vector multiplication. However, I cannot compile and I don't...
  47. B

    Finite Dimensionality of Endomorphism Ring in Simple Modules?

    Let R be a finite dimensional C-algebra (C=Complex numbers) and S a simple R-module. Why does it follow that End_{R}(S) is also finite dimensional (as C-vector spaces, I'm guessing)? I'm not really sure how to construct a basis for it using one of S, and there's probably another reason for it...
  48. A

    Predicting Output from Triple Module Redundancy System

    Referring to figure Q5, which shows triplemodule redundancy, assume that each module is configured to calculate the same function y=f(x) on 16bit input word x. Without knowing what is the value of x, and without knowing the exact function f() that each module implements, determine the most...
  49. P

    Is it possible to convert heat to electricity using Peltier Module?

    I need to know because i need a chip that is a conductor and absorbs heat then converts it to electricity.
  50. M

    Fortran How can I fix the Fortran module problem with gfortran?

    Hi! I am writing a simple code to get familiar with creating Fortran module. The program consist of a main.f and a module.mod file. When I type in: gfortran main.f I get the following error: Fatal Error: File 'module.mod' opened at (1) is not a GFORTRAN module file I think I found the...
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