What is Modules: Definition and 224 Discussions

Broadly speaking, modularity is the degree to which a system's components may be separated and recombined, often with the benefit of flexibility and variety in use. The concept of modularity is used primarily to reduce complexity by breaking a system into varying degrees of interdependence and independence across and "hide the complexity of each part behind an abstraction and interface". However, the concept of modularity can be extended to multiple disciplines, each with their own nuances. Despite these nuances, consistent themes concerning modular systems can be identified.

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  1. E

    Good book on linear algebra over rings (i.e. modules)

    Can anyone recommend a book that covers linear algebra through the perspective of modules? I am basically trying to find something that would highlight all the differences between modules and vector spaces. Lam has written the book Lectures on Rings and Modules, which is good, but doesn't...
  2. C

    Installing perl modules on Ubuntu

    hi everyone, I'm trying to install the following Perl module: mod_perl-2.0.4 And I've been trying to following these directions (specifically, the "if you're on UNIX" section): http://www.cpan.org/modules/INSTALL.html Now, I extracted the files and placed the new directory into my perl5...
  3. B

    Can Direct Sum Isomorphism Imply Module Equality in PID?

    Hi. I'm trying to prove this "little fact": let M, N be finitely generated modules over a PID. Then if M+M=N+N (where = means isomorphism and + means direct sum) then M=N. I'm sure it can be done with the structure theorem (it is obvious from the hypotheses); it looks like it should be...
  4. O

    Multiple gsm modules, one antenna

    hi everyone, a friend of mine bought a multi-sim iphone clone from china. i was so amazed at this. as a hobbyist, i want to create my own pc-based multi-sim gsm terminal. so i want to use 4 gsm modules(sim300). one for each gsm-provider here in my country. but my problem is i want to use only...
  5. T

    Galous Group Modules Self Study: Q&A

    I was doing some self study and have questions: 1. p(x)=x^{7}+11 over Q(a), R. where a is 7-th root of unity. What are Galouis groups? For the 1st case I got Z_{7}, second not sure. need hint for that 2. need hint. I know it is easy: M is an R-module. Show that Hom_{R}(R,M)\congM. 3. Spse...
  6. F

    Modules & Ideals: A Closer Look

    General question: Is there some relationship between vector spaces/modules and ideal of a ring? In both vector spaces/modules and ideals, we have closure under addition and also it "swallows" elements from the field and ring, respectively.
  7. H

    Why is M Torsion-free & Rank 1 but Not a Free R-Module?

    Hi all, I came across this problem in a book and I can`t seem to crack it. It says that if we have an integral domain R and M is any non-principal ideal of R, then M is torsion-free of rank 1 and is NOT a free R-module. Why is this true? cheers
  8. S

    Action of a cyclic group on modules

    Homework Statement Let G = <x> be a cyclic group of prime order p and let M be a vector space over \mathbb{Q} with basis S = \{m_0,m_1,\dots,m_{p-1}\}. G acts on the S in a natural way by cyclic permutations and this action is linearly extended to an action of G on M. Now, the resulting...
  9. M

    Proving HomR(F;M) isomorphic to M^n for Free Modules of Rank n < 1

    Let R be a commutative ring with 1. If F is a free module of rank n < 1, then show that HomR(F;M) is isomorphic to M^n, for each R-module M. I was thinking about defining a map Psi : HomR(F;M)--> M^n by psi(f) = (f(e1); f(e2); ... ; f(en)) where F is free on (e1; ... ; en) and show Psi is...
  10. O

    Terminology issue regarding modules and representations

    Homework Statement Given a field F, FS4 is a group algebra... we have a representation X that maps FS4 to 3x3 matrices over (presumably) F. Let V denote the FS4 module corresponding to X... do stuff. My question is, what the heck is V supposed to be? I assumed that V is F3, but that...
  11. M

    What Is the Closure of Modules Theorem in Several Complex Variables?

    can anyone give me a precise statement of the "closure of modules" theorem in several complex variables? it says something like: a criterion for the germ of a function to belong to the stalk of an ideal at a point, is that the function can be uniformly approximated on neighborhoods of that point...
  12. Ed Aboud

    Choosing Elective Modules for Theoretical Physics Program

    Hi all. Starting an undrgraduate programme in Theoretical Physics in two weeks and I have to choose two modules to take for the year. These modules can be of absolutely any topic that is availible in my college, they are called elective modules. I have come to a conclusion that it probably...
  13. P

    Proving Projective Modules Have Free Modules as Direct Sums

    Please help me to prove that for a projective module P there exists a free module F, such that P +F =F. Here + denotes direct sum = denotes isomorphic. Thanks
  14. P

    Proof of Semisimple Modules: Finite Summands & Finite Generation

    Can somebody help me with the following proof: Let M be a semisimple module, say M = +_IS_i, where + denotes direct sum and S_i is a simple module. Then the number of summands is finite if and only of M is finitely generated. I have problem with understanding the proof of the following...
  15. quasar987

    Proof of Theorem 1, Chapter 12: Modules over Principal Ideal Domains

    [SOLVED] Algebra - modules Homework Statement I'm reading this proof from D&F and there's something I don't get. It is theorem 1 of chapter 12 on modules over principal ideal domains. The theorem is the following "Let R be a ring and let M be a left R-module. Then, (Ever nonempty set of...
  16. P

    Torsion Modules & Finite Generation: Investigating the Connection

    Homework Statement Does a torsion module M imply M is cyclic? Or does it imply M is finitely generated? I think cyclic implies torsion module. What about the reverse? The Attempt at a Solution I think there is a connection but don't see it.
  17. P

    Are All Modules Merely Vectors, or Do They Vary by Type and Operation?

    I know there are many examples of rings like R[x], N, Q, where the elements can be fundalmentally different like polynomials and numbers. But are there different type of modules like there are rings? Or are modules just any vector? And the modules are different when you consider which R...
  18. P

    Modules & Algebra of Matrices: Intro Book Recommendations

    Anyone recommand readable intro books on modules and algebra of matrices?
  19. A

    Question regarding finitely generated modules

    I am supposed to show that the following are equivalent for a finitely generated module P: 1. P is Projective 2. P is isomorphic to direct summand of a free module (There are 2 others but they refer to a diagram) I am stuck on showing 1 => 2. I know that since P is projective there is...
  20. M

    Finite Modules and Surjective Endomorphisms: An Elementary Exploration

    In the spirit of challenges, here is a surprizingly simple question about finite modules, that I did not know the answer to until recently. It is so elementary that I suspect it was common knowledge to the ancients and only forgotten as algebra became more sophisticated. We all know that...
  21. G

    Schools Advice on interesting related physics modules at university

    Hi all, Im a bit new to this forum. I will be going to university this September (Hopefully) and i decided to do a masters degree in Straight MAthematics. I have decided for some of my options that i will do some programming courses as i enjoy logic behind programming. But I am also...
  22. S

    Guidance on Level Physics Modules

    Help CHOICES !lol i am studying for a level physics and don't really know which module to take on for the summer exams. i have looked at past papers but they haven't helped me much and it is still holidays. i need to be able to find the one i want to do so i can start the topic. i don't...
  23. C

    Modules with multiple operators

    Consider the set of 2x2 matrices which form a ring under matrix multiplication and matrix addition. \mathbb{R}^3 is module defined over this ring. So, we have three dimensional vectors whose elements are 2x2 matrices. My question: Can I also define another "scalar multiplication" that...
  24. Ivan Seeking

    Reprogramming fuel injection modules

    I have a buddy asking if I can do this for his 300 ZX. I have checked and there is a programmable module available with software, but apparently some companies [one at least] are reprogramming the factory chip directly. Does anyone know where to get the code, or at least what values affect...
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