What is module: Definition and 167 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. mishima

    Help me understand cheap boost module?

    Hi, I recently acquired some of these cheap modules for plasma experiments. I tried dissolving the epoxy off of one of them in an attempt to reverse engineer the circuit. I can see a resistor, diode, and transformer but am unsure about some of the other components. I was wondering if anyone here...
  2. S

    I Definitions of torsion element

    The current Wikipedia article on Torsion element (https://en.wikipedia.org/wiki/Talk:Torsion_(algebra) ) says: A ring R can be used to define a module M of the ring over itself. Multiplication of a module element m by a ring element r is the same as multiplication in the ring. If m is not...
  3. matqkks

    What to cover in a differential equations module?

    I will have to teach a first course in differential equations. What should I cover in this module? For example, in most books they have Laplace Transforms which is fine but I would not use LT to solve differential equations. I want to write a course that it motivates students and has an impact...
  4. Euge

    POTW Support of a Finitely Generated Module

    If ##R## is a commutative ring with ##1## and ##M## is an ##R##-module, the support of ##M## is defined as ##\operatorname{Supp}M = \{\mathfrak{p}\in \operatorname{Spec} R\mid M_\mathfrak{p} \neq 0\}##. Show that if ##\phi : R \to S## is a ring homomorphism and ##M## is a finitely generated...
  5. S

    Python Pytest, unittest : Mocking out a non-existent imported module

    The following provider module imports a_missing_module and implements a helper_function. (I haven't put in any code that actually uses the missing module, but there could be such code in general). # provider.py import a_missing_module def helper_function(): return 999 Now this client...
  6. K

    B Definition of Super Lie Module

    Hello! I have some troubles with the definition of the so called super Lie module. In Alice Rogers' textbook "Supermanifolds theory and applications" definition goes as follows Suppose that ##\mathbb{A}## is a super algebra and that #\mathfrak{u}# is a super Lie algebra which is also a super...
  7. F

    Prove a CG module is irreducible

    Proof: We first show ##W## is a ##\mathbb{C}G## module. Let ##u = 1 + \omega^2a + \omega a^2## and ##v = b + \omega^2ab + \omega a^2b##. It is enough to show ##ua, ub, va, vb \in W##. We have\begin{align} ua &= a + \omega^2a^2 + \omega \\ ub &= b + \omega^2ab + \omega a^2b \\ va &= ba + \omega^2...
  8. F

    "import" in Jupyter notebook not working with notebook module....

    Hello everyone, I am writing Jupyter notebooks which are essentially JSON files. I wrote a custom module called module001 containing some functions and saved it as a .ipynb file. Upon importing the module into a different notebook using the instruction import module001, I received the error...
  9. M

    Comsol: Infinite Element Domain module

    Hello folks, I want to simulate a 2D heat transfer process in the subsurface on a region which is infinite on the r-direction. So, as you know, the very basic way to model this is to draw a geometry that is very long in the r direction. I have done this, and the results that I obtain is correct...
  10. S

    Is a Continuous Mars-Earth Transporter Using Gravity Assist Viable?

    I watched a movie a while ago (i think it was called Stowaway) where there was a craft with artificial gravity, and enough space for everyone's needs that was continuously going between Mars and Earth gravity assist slingshotting around them each passing. And then the crew just used a small...
  11. H

    A I am looking for an example of a Fredholm module

    I found this in wikipedia It only gives the definition of a Fredholm module. so i would like to find simple examples. what is this hermitian involutive F? thanks
  12. V

    LED module failing due to DC motor?

    I use a 2 Relay Motor module to control Direction on a motor (linear actuator). When Relay A is active, actuator retracts. When Relay B is active, actuator extents and Led Module is activated. After some repetitions Led module fail. Cause of the fail? I believe Surge voltage, although i am not...
  13. sodoyle

    How to define PV module IV curve using given parameters

    I am looking at a solar panel and would like to be able to plot the IV curve for it. I have Isc, Voc, Imp, and Vmp from the datasheet so I can get the fill factor. I know each cells dimension and the number of cells too so I can find the current density if required. Is there a way to use the...
  14. J

    Can you add a wifi module to a Samsung S8?

    My Samsung S8 has a weird problem. The wifi is not working. After bringing it to official Samsung Service Center. They tried fixing the firmware and software. But it didn't fix it. They said they couldn't fix the wifi module because it is inside the motherboard so have to replace the entire...
  15. Eclair_de_XII

    Python Hexadecimal errors when hitting back-space while using inquirer module

    I'm using this user-defined module for an amateur coding project, and I am using 'Text' from the 'inquirer' module. When I am either inputting things, or whenever I am validating things, I always get some sort of error. These errors mainly result whenever I hit the back-space key on my...
  16. Lord Crc

    Signal classification and processing for a gesture sensor module

    I got a gesture sensor module that produces a signal per event. The each signal is a set of regularly sampled readings from four photodiodes. The number of samples per event can be very different, from around 20 up to over 100, and each sample value is essentially the measured brightness...
  17. I

    AS-Interface control cabinet module

    Hello everyone, can somebody please explain me what is the function of this relay. I can't understand it from their datasheet. Thanks. https://www.ifm.com/ua/en/product/AC2258?tab=details
  18. F

    Is Turtle a Module or Library in Python?

    Hello, I am trying to fully understand the difference between module, library, and package in Python. I think a module is a single file with a specific functionality. A library is like a directory: it contains multiple files, i.e. multiple modules. A package contains multiple libraries and...
  19. M

    Programs Module Choice advice for a theoretical physics degree (Durham)

    I'm starting at Durham on the 29th of September and I need to get my module choices sorted. I have the choice between 40 credits of maths modules designed for scientists, and 40 credits of maths modules done by regular maths students. They say that you should only do the regular maths modules if...
  20. saroj34

    What is your opinion about using the ELB-REV4 camera module with Simpl

    I have no previous experience using this tool. My question is if some of you have any comment about this tool or any option for image processing using similar cards such as arduino, etc.
  21. matqkks

    MHB Order Matters: Intro to Pure Mathematics Module

    I want to produce a resource that has a narrative and includes the following topics: Sets, logic and proofs, numbers (irrational, integers, rational, …), binomial theorem, geometric series, inequalities, define things like identity, polynomial, symmetry, sigma and product notation. It is in aid...
  22. ChadThePianist

    COMSOL Modeling help (ambient air around a thermoelectric module)

    Hello everyone, I am wondering how to model ambient air around a thermoelectric module in COMSOL. I am fairly new to the software and am doing undergraduate research revolved around it. Any help or pertinent examples would be appreciated. I can send/post screenshots and or .mph files if it would...
  23. B

    Comp Sci Dynamic Link Library, Compaq Visual Fortran 6.6 & Module

    Dear Forum Members, I need to create and use dynamic-link library (DLL) for Fortran application using Compaq Visual Fortran 6.6. The following code works just fine: ########################################### PROGRAM AMAIN1 IMPLICIT NONE REAL(8):: A,B,S A = 1D0 B = 2D0 CALL SUBRO1(A,B,S)...
  24. S

    Using The ESP8266 Wifi Module Mini

    Hey guys, quick question on this module.The manual states " 5V-3.3 converter onboard for operation from USB" Does this mean that i can power the board straight from my computer without error from "overloading" the board.i ask this because a lot of other modules such as these don't work like...
  25. T

    I An Embarrassing Question about turning a ring into a module

    Given a ring R, how exactly do I interpret it as a module? A lot of my homework assignments involve treating a ring as "a module over itself" and I don't know precisely what that means.
  26. Math Amateur

    MHB Book on Ring and Module Theory ....

    I would be grateful for opinions on the following book as a good advanced undergraduate/ beginning graduate book for self study ... "Graduate Algebra: Commutative View" by Louis Rowen ... (American Mathematical Society, 2006)Conveniently Louis Rowen has published a book for a "first course" in...
  27. Math Amateur

    MHB Submodules and Factor Modules of a Noetherian Module .... Bland, Proposition 4.2.5 .... ....

    I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.2: Noetherian and Artinian Modules and need some help to fully understand the proof of part of Proposition 4.2.5 ... ... Proposition 4.2.5 reads as follows: https://www.physicsforums.com/attachments/8189My...
  28. Math Amateur

    I Submodules and Factor Modules of a Noetherian Module ....

    I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.2: Noetherian and Artinian Modules and need some help to fully understand the proof of part of Proposition 4.2.5 ... ... Proposition 4.2.5 reads as follows: My questions are as follows:Question 1 In the...
  29. M

    Writing a module to a linux kernel

    I was wondering about "writing a module to a linux kernel." This question haven't asked yet. Would you please explain why linuxers write such modules to a linux kernel? What is the reason? Thank you.
  30. G

    MHB Problem about equivalent conditions for a basis of a free module

    Here's the problem: I don't see why there should be only finitely many nonzero a_z in b. I was able to prove uniqueness assuming that there only finitely many nonzero. I was able to show b implies d and b implies c, c implies a.
  31. ZMacZ

    Revolutionizing Space Travel: The Innovative Design of the Circular Module

    When I see stuff on Netflix (yes not real), and yet I look stuff up on the Net (real) and they try and create a spaceship capable of travellng anywhere else in the solar system, they always come up with standard missile design and go "new and improved.." When they then show failure to actually...
  32. thegreengineer

    PIC Microcontrollers: problem with LCD module (see below)

    Good morning people. Recently I started programming in assembly language my PIC16F877A. Success. Now I wanted to work with a LCD display (more specifically a 16x2 LM016 display). At first I did not know the commands until I saw a datasheet and this page...
  33. R

    Other A module choice between Cosmology and Fluid Mechanics....

    Hi all, I study Mathematics and Theoretical Physics at university. Next year, I'll have a choice between three modules; Thermodynamics and Statistical Physics Cosmology Fluid Mechanics My main interest is Condensed Matter Physics; therefore, thermodynamics and statistical physics is a given...
  34. S

    MHB Please help me understand my Credit Card Module Project

    This is the worksheet my quantitative reasoning teacher assigned us. I was able to complete the chart using Microsoft Excel and printed a page that has all the values for to table in with the table. A tutor at my college gave me the logical formula to find the minimum payment, interest, and...
  35. Robertphysics

    Ultrafast bridge rectifier module question

    Hi , I have a 50khz square wave from a smps transformer and currently I am using MUR 1620 fast diodes but since they come in individual trasistor type TO220 type packages I have some problems with attaching them properly to heatsink , does anyone know are there any nice diode bridge modules like...
  36. Fyj

    Studying Take module on Quantum Computing or Stochastic Mechanics?

    Hi. I was wondering if you could help me out a bit here. I have a choice to take either a module on stochastic dynamics in statistical mechanics or quantum computing for my masters. Both seem really interesting so it’s a close tie between which one has more current/future applications. The...
  37. Divya Shyam Singh

    Why is the addendum of the gear kept equal to the module?

    In general calculations of gear design, addendum is taken as a factor of the module of the gear such as equal to module or 0.8 times the module and dedendum is taken as 1.25 times the module. Why are both these defined in terms of module? How did we reach to this conclusion?
  38. S

    Protection on Step up and Step Down Converter Module Bucks

    In a circuit that I'm building, I have a power source of 5 volts DC that powers various components. A few of them are LED lights and light bulbs. -Background Info- In circuit 1, I have a step up buck "2A DC-DC boost step-up Conversion module MicroUSB 2-24V 3V to 5v-28V 12v 9v 24v"...
  39. Math Amateur

    I Module Over a Division Ring - Blyth Theorem 1.1, Part 4

    I am reading T. S. Blyth's book "Module Theory: An Approach to Linear Algebra" ... ... and am currently focussed on Chapter 1: Modules, Vector Spaces and Algebras ... ... I need help with an aspect of Theorem 1.1 part 4 ... Theorem 1.1 in Blyth reads as follows: In the above text, in part 4...
  40. Math Amateur

    MHB Module Over a Division Ring - Blyth Theorem 1.1, Part 4

    I am reading T. S. Blyth's book "Module Theory: An Approach to Linear Algebra" ... ... and am currently focussed on Chapter 1: Modules, Vector Spaces and Algebras ... ... I need help with an aspect of Theorem 1.1 part 4 ... Theorem 1.1 in Blyth reads as follows:In the above text, in part 4 of...
  41. A

    RF Module Communication for Hobby Project: Using TTL or Encoders/Decoders?

    For a hobby project I got a couple of RF modules, a QAM rx2 433 receiver and a DSQAM tx1 transmitter. I understand they need some kind of TTL to work, would just using some NAND gates hooked up to the transmitter and receiver be enough or do I need something more fancy like encoders and decoders?
  42. S

    Efficiency of a PV module and solar thermal collector

    Does the efficiency of a PV module and solar thermal collector go down as ambient temperature (outside temperature) increases? I know there are other factors that influence efficiency, but I'm only considering the one parameter of temperature on a PV module and solar thermal collector.
  43. Z

    Voltage output from DAC module, Obtaining the Pk-Pk Value

    I have a sine wave produced as an output, which varies. This sine wave has been filtered by a moving average filter. From this output, coming out of a DAC module, I need to obtain the the voltage peak-peak value and store it preferably in an array. How can I do this? More importantly how can I...
  44. D

    100um Core MM Fiber connected to 50um Core 10G SFP Module

    I have two systems that are approx. 300-400ft apart that I am connecting via a 10 Gig fiber connection. The fiber I am using is a 100um core MM fiber and the switches will be using a 50um core OM4 (4700 MHz*km) SFP module. Is there a way to find out what type of loss I should be expecting, is...
  45. Rediska

    GENIE 2000, LabSocs module, Detector.txt

    Dear all, I am trying to use built in LabSocs detectors for sourceless calibration of our laboratory detector. In order to quantify possible differences, I wanted to extract the exact geometry of the model, that is presented inside LabSocs. Since my version of the software is very limited, I...
  46. rushi121

    How to find a right RF module for a project?

    I am a product developer but not an electronics engineer. I am doing a cost analysis of a product idea for my company. The product will need something like this... There will be two small portable devices (A and B) 1 meter apart (not in line of sight since A can be in pocket). Product A will...
  47. evan manalu

    Circuit inside DC boost step up pulse power module

    Any one know circuit inside DC boost step up pulse generator? I have this one buy from ebay 400Kv type,i want to know how this work by circuit inside.. I had googling and not found result.. Please help me..
  48. F

    Solenoid Suppressor Module: What is it and How Does it Work?

    I was troubleshooting a solenoid valve,and had wired a device that look like an capacitor.I did a research on the info on it.,and it was a suppressor module.
  49. N

    How to install the serial module into cygwin (terminal)

    Dear group, I downloaded this software "cygwin," (terminal), and trying to run Python on this software but i failed on the installing the serial, Could you please give me some ideal? Thank you, Nate Duong.$ python Blinking_off.py Traceback (most recent call last): File "Blinking_off.py"...