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. ChristinaJ

    Mathematica Mathematica: Module inside For loop

    Hi all, I have the following code which runs without error but gives no output. It's probably simple but I just can't see the problem. LM={}; M[line_, cur_, lq_, ld_, k_] := For [i = 1, Length[line[[1]]], i++, Module[{m}, If[line[[1, i]] == "Q", m = {{Cos[k*Sqrt[Abs[cur]]*lq]...
  2. H

    Fortran Fortran Module w/ user defined type

    I have a bunch of programs that initialize values of variables of a user defined type, so I thought I'd initialize them all in a module and have each program 'use' the module. But, it seems the only way to initialize the variables in a module is to put the initializations in a subroutine within...
  3. S

    Comsol 4 Plasma Module: Temperature Limitation?

    I'm using comsol 4 for plasma modeling but I've read that this module is just for low temperature plasma, does anybody knows the temperature limitation of the plasma in this module? I mean how much is the upper limitation of plasma temperature?
  4. K

    Mathematica Mathematica: looping using Module

    Dear all, I have difficulty to solve this code which involves looping, In [1] := m = 1; n = 1 ; A = -1 ; B = 5 ; In [2] := m = 1; n = 3 ; A = 8 ; B = -2 ; In [3] := m = 1; n = 5 ; A = 9 ; B = 7 ; In [4] := m = 3; n = 1 ; A = -2 ; B = 8 ; In [5] := m = 3; n = 3 ; A = 4 ; B = 3 ; In...
  5. M

    Maximum jerk for experimental module

    Maximum "jerk" for experimental module 1. A landing module has a mass M with three springs each of stiffness k that hover over the surface (height not given). If the final touchdown velocity is to be Vtd, what is the maximum jerk (time rate change of acceleration) the module experiences given...
  6. K

    Mathematica Mathematica: working with Module for 2 variables.

    Dear all, Iam running a code which has only 2 main variables, i.e. m and n using Module. I have tried to run the code as attached but it is not working. Please help me to improve the code so that I would be able to get qmatrix[m,n]. Perhaps, is there any other better method to use or...
  7. quasar987

    Free finitely generated module has finite rank?

    How does one prove that for R commutative, a free finitely generated R-module has finite rank? If R is a field (i.e. in the case of vector space), then we can argue that given a finite generating set S={s1,...,sn}, if S is not linearly independent, then, WLOG, it is that (*)...
  8. I

    Smallest submodule of module

    Homework Statement Let S = \{v_{},...,v_{n}\} be a subset of a module M. Prove that N = <<S>> = \{r_{1}v_{1} + ... + r_{n}v_{n} | r_{i} \in R, v_{i} \in S\} is the smallest submodule of M containing S. First you will need to formulate precisely what it means to be the smallest submodule...
  9. I

    Is IM a Submodule of M?

    Homework Statement Let M be a R-module and I is an ideal in R. Let IM be the set of all finite sums of the form: r_{1}v_{1} + ... + r_{n}v_{n} With r_{i} \in I and v_{i} \in M Is IM a submodule of M? Homework Equations A submodule of an R-module M is a nonempty subset S of M that is...
  10. J

    Can a Bluetooth Module's Range be Configured and What are the Options?

    Hi guys. I am new here. Is there a bluetooth module which you can configure the range of the the module? For example from a 5 meter range to about 1 ft or less... Currently planning on using BTSerial1 Bluetooth module. Any idea of a less expensive and better bluetooth module? Im new to this...
  11. C

    What's the Best Module Selection for Pursuing Theoretical Physics After BSc?

    So basically I want to go further into theoretical physics after my BSc. But I don't know what modules would be the best choice. The University I applied for only offers the following module choice, but they state that if I want another selection, the Dean must approve it. 1st year...
  12. A

    Mathematica Need some assistance with Mathematica Module

    I am currently working on an algorithm which will ultimately be able to take as input a 3 matrices, (R,G,B) and convert each pixel value into hue saturation and intensity values. So far I have been able to get all but the hue portion to work properly. Here is the code thus far...
  13. A

    Finding the Right Module for Spur Gears

    hello, i am doing gear calculations my problem: i get several point numbers for the module of the spur gear din 780 suggest a standard table with modules so i just have to wrap up my calculated modules, for example: 3.91 => 4 ? thank you vm !
  14. J

    Maths needed for a plasma physics and astrophysics module

    Hi, i'm studying a MEng Electrical and Mechanical engineering course in the UK. I've just started second year and have been approved by my advisor to take on an extra module next semester in plasma and astro physics. This module is intended for 4th year physics students and won't count...
  15. A

    Complex number argument and module

    Homework Statement z=\frac{(1-3i)^{100} * i * (7-5i)}{5+7i} Homework EquationsFind module and argument of z. The Attempt at a Solution Assuming: |z_1 * z_2| = |z_1||z_2| |z|=\frac{|1-3i|^{100} * |i| * |7-5i|}{|5+7i|} And now calculate each module individually by "Pythagoras theorems"...
  16. F

    Landing the Lunar Excursion Module: Astronaut Training Simulation

    You are in training to be an astronaut. In one of your training simulations, your goal is to land a lunar excursion module (LEM) on the surface of the Moon. This LEM has two rocket engines attached to the center of the craft. The engines typically point at angles of 22.0° in opposite directions...
  17. B

    Module Equivalence: Understanding Ann(M)

    Module "equivalence" There is a problem in a book I'm not quite understanding. Let M be an R-module and let I=Ann(M). Show that M can be regarder as an R/I-Module where scalar multiplication is given by the rule m(I+r)=mr I don't understand what they mean by "regarded as". Am I suppose to...
  18. P

    Showing every free module is Projective

    Take P a free module over an arbitrary ring. Show P is projective. Definition of Projective: If f: M-->N and g: P-->N are module homomorphisms with f surjective, then if P is projective there exists homomorphism h such that h: P-->M with f(h(x))=g(x) for all x. Obviously f has a right...
  19. F

    Usb based data acquistion module, and interfacing it with labview?

    I want to make my own usb based data acquistion module, and try interfacing it with labview? Now I have a few questions, since i am quite new to it: Where do I get started? Can I do the interfacing(with labview) via parallel port ? or serially ? Can the Module be made using PIC...
  20. G

    Few questions about homemade IrDA module

    First of all, I'm not an electrician, I'm a medical student who occasionally grab a soldering iron for some fun. So if I'm asking something really stupid, I'm sorry. I found scheme forIR transciever on http://www.hardwaresecrets.com/article/86/2 and I'm plannig to build it. I was wondering is...
  21. F

    Linear Momentum - Module and Shuttle Go Boom

    Homework Statement A 500.0 kg module is attached to a 400.0 kg shuttle craft, which moves at 1000 m/s relative to the stationary main spaceship. Then a small explosion sends the module backward with speed 100.0 m/s relative to the new spaeed of the shuttle craft. As measured by someone on the...
  22. I_am_learning

    Need suggestion in developing an electric password module

    I am trying to build an electric password box that will trigger a relay when correct order of password is pressed (via push buttons). I am going to use the relay to open the main door of my home electrically (via motors). So if you have any suggestion for the password box, it will be of great...
  23. O

    Ambient Power Module - Questions & Answers

    Hi Does anyone have any experience with ambient power modules? I have a few questions, if anyone could answer any of them i would be most apreciative. 1) do they work? 2) how much power can they output? 3) how small can you make them? 4) how much could you make them for (in mass...
  24. wolram

    Oopic module to control a robot

    I have just bought an oopic module to control a robot, the problem is the cable for programing has a plug that will not fit into my laptop. http://www.oopic.com/pricing.htm Is there a way around this?
  25. L

    Module of Vector Sum: 3V2in, 3cm, 6cm & 5cm

    Determine, using the vector components, the module of the vector sum of the four vector data in the figure. Consider = 3V2 inches, b = 3 cm, c = 6 cm and d = 5 cm. Adopt: sin α (alpha) = 0.60; cos α (alpha) = 0.80 and sin 45 degrees = cos 45 degrees = V2/2...
  26. A

    High Voltage Module for Capacitor Charging

    I just ordered a DC to HV DC converter (the F40 model, datasheet here: http://www.emcohighvoltage.com/Fseries.PDF ) from eBay for $50. My intent is to charge capacitors such at the 400V 12,000uF one located here http://www.amazing1.com/capacitors.htm. The converter has output up to 4,000V...
  27. N

    Good idea to do a language module in my MEng degree?

    I'm soon starting my 3rd year of my degree. Were allowed to select our modules now, and basically decide what we want to go into, i.e. fluids/thermo, materials, stress analysis etc. Were also given the opportunity to choose one module that is not engineering related. I was thinking about doing a...
  28. S

    Torsion Module M with ann(M)={0} and Integral Domain R | R-Module Notations

    Notations: M denotes an abelian group under addtion R denotes a commutative ring with identity ann(?): Let M be an R-module and r∈R v∈M, then ann(v)={r∈R | rv=0} Terms: R-module: a module whose base ring is R torsion element: A nonzero element v∈M for which rv=0 for some nonzero r∈R...
  29. C

    Seperation prcoesses fundamentals module

    Hi I am curently doing my degree in chemical engineering and I'm finding the separation processes module a bit rough, mainly because of interuption to lectures and the lecturer not being there most of the time. Anyway I've got an exam coming very soon and need some help, getting desperate! A...
  30. R

    COMSOL RF Module: Seeking Help on IR Heating

    COMSOL RF module: urgent Hi i am a new user to comsol RF module. Actually I a want to model the heating of a material using IR waves... can i use the RF module (which illustrates microwave heating as an example) to model the IR heating...do we have options to change the frequency of wave from...
  31. S

    COMSOL-nanoparticles-PML-scattering formalism in RF module

    Hi, all, I am starting with calculating scattering cross sections of metallic nanoparticles. I have some doubt about what type of scattering boundaries conditions and PML to use, since near field shows some surface waves on PML´s inner side and some reflections which affect my far-field...
  32. R

    Help needed in COMSOL3.3a-heat transfer module

    urgent help needed in COMSOL3.3a-heat transfer module hi friends... I am doing a heat transfer problem in 3D...I have designed a heating device in micro range (exactly similar to the heating device in component library) and kept 3 layers of blocks of material (Si, SiO2, Fe ). I am confused...
  33. quasar987

    Why Can't a Module Have Finite & Infinite Basis?

    Why couldn't a module have a finite basis and an infinite one?
  34. J

    HiI've started a mechanics module and just wanted to know, what is

    Hi I've started a mechanics module and just wanted to know, what is the difference between Young's Modulus ('e') and the E = Stress/Strain? Thanks! Jase
  35. G

    Module action sends zero to zero?

    Hello, Excuse me if I ask something obvious here, but I can't prove it.. Say R is a ring and M an R-module. So, 0 \in M as M is an abelian group. I guess r0=0, no?! Can you tell me how we prove that? Again, sorry if I ask something obvious..
  36. O

    Need help with Comsol (Heat Transfer Module)

    Hi! I have this problem. I have a cylinder filled with a hot Nitrogen gas (340 K) under 3000 psi pressure. The cylinder is exposed to the air and I need to find a temperature distribution in this system as a function of time. I am using Heat Transfer model -> Non-Isothermal Flow. The...
  37. P

    Mathematica Beginner to Mathematica's question using Module

    Okay, this is the question that i need to solve using mathematica: Define the function f(n) which counts the number of zeros in n if n is the integer greater than 0. If you input 105, 1005, 10005, find f(n). I want to use Module in this question and I just found out that i have to use...
  38. O

    Is this really a module?

    Homework Statement K is a field with finite characteristic p, G is a finite group, and W is a set that G acts on transitively (so for all x,y in W, there exists g s.t. gx=y). It then says consider M=KW the permutation module. What is KW supposed to mean? I know for a group G that KG is...
  39. F

    Experience in RF module Comsol?

    Hello, anyone with some experience in Comsol? I have a few basic questions on the RF module thanks!
  40. P

    Prove Simplicity of R-Module V & Find Jac(R) & isomorphism R + R

    Let V be a countable dimensional vectorspace over a field F . Let R denote End_F V . Prove that V is a simple R-module. If $ e1 , e2 , . . .$ is a basis of V , then we have a module homomorphism φ_j from R to V , sending f in R to f (e_j ). Find the ker(φ_j) . Find Jac(R). here I...
  41. P

    My definition of an artianian module is : A module is artinian if

    My definition of an artianian module is : A module is artinian if every decending chain of submodules terminates. Let A be a semisimple ring and M an A-module. If M is a finite direct sum of simple modules then M is artinian. Proof: Suppose that M= S_1+...+S_n where + denotes direct...
  42. G

    The module is injective iff it is a direct summand of an injective cogenerator

    could anyone give me a proof of this statement: The module is injective iff it is a direct summand of an injective cogenerator.
  43. P

    Calculating Apollo 13 Command Module Drag Coefficient

    So, after looking at all the stuff those geniuses up at NASA came up with, I'm trying to figure out how to get the drag coefficient for the Apollo 13 command module reentry. Heres the stuff I thought were important: Entry-interface 400,000 ft 36,129fps Drogue chutes deploy at...
  44. M

    Prove: If N Is Pure, Then N Is a Direct Summand of M

    Homework Statement Suppose M is a D_module and N is a submodule. N is called pure iff for any y \in N and a \in D ax = y is solvable in N iff it is solvable in M. N is a direct summand of M iff there is a submodule K with M = N \oplus K. Prove: (1) If N is a direct summand, then N is pure. (2)...
  45. M

    Prove: Module & Submodule Homework

    Homework Statement Suppose M is a D_module and N is a submodule. N is called pure iff for any y \in N and a \in D ax = y is solvable in N iff it is solvable in M. N is a direct summand of M iff there is a submodule K with M = N \oplus K. Prove: (1) If N is a direct summand, then N is pure. (2)...
  46. M

    Apollo 1 command Module Pressure/Force

    Homework Statement What would have been the force on the hatch of the Apollo 1 command module (Before the fire) during the "plugs out test" Homework Equations more info 14.8 PSI of pressure outside of the module and 17.5 PSI 1 PSI= 6 894.75729 pascals. 14.8 x 6894.74=102 042.152...
  47. U

    Maximize Your GCSE Biology Grade: Tips for Success on March 5th Test

    anyone got any tip before the test?? it will happen at march the 5th what is the best way to achieve my best grade possible?
  48. M

    More group theory (or module theory)

    Homework Statement Given an abelian group G with generators x and y, and relations 30x + 105y = 42x + 70y = 0, show it's cyclic and give its order. Homework Equations The Attempt at a Solution I'm guessing the proof basically involves cleverly adding 0 to 0 to show that x = ry or...
  49. S

    Power calculation of a PWM Module

    Hi.. How to calculate the power rating of PWM pulse train? Reg, Sridhar
  50. P

    Finding a Basis for a Module: Techniques and Examples

    Homework Statement Given a few vectors that span a module space, how do you find a set that is a basis for this spanned space consisting of entirely different vectors to the original spanning vectors? The Attempt at a Solution I assume you find what kind of space is spanned by the...
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