Modules Definition and 214 Threads

I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). I need help with understanding Example 2.1.3 (ii) (page 39) which concerns $$L$$ as a submodule of the quotient module $$ \mathbb{Z}/p^r \mathbb{Z}$$ ... ... Example 2.1.3 (ii) (page...

I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). At present I am focussed on Chapter 2: Direct Sums and Short Exact Sequences. Example 2.1.2 (i) on pages 38-39 reads as follows:https://www.physicsforums.com/attachments/2957 In the...

I don't see why not but is there any reason that i could not use these modules http://www.ebay.com/itm/121370353437?ssPageName=STRK:MEWAX:IT&_trksid=p3984.m1423.l2649 to make a wireless link between this camera and screen...

I am reading Dummit and Foote Chapter 10: Introduction to Module Theory. After defining modules and giving some examples, D&F state the following: "We emphasize that an abelian group M may have many different R-module structures even if the ring R does not vary ... ... " I am puzzled by this...

I am reading Paul E. Bland's book, Rings and Their Modules, Section 2.1: Direct Products and Direct Sums. I have a question regarding the proof of Proposition 2.1.1 Proposition 2.1.1 and its proof (together with with a relevant preliminary definition) read as follows: As can be seen in the...

I am reading Paul E. Bland's book, Rings and Their Modules. In Section 2.1: Direct Products and Direct Sums, Bland defines the direct product of a family of modules. He then, in Proposition 2.1.1 shows that there is a unique module homomorphism (or R-Linear mapping) from any particular R-module...

I am reading Paul E. Bland's book, Rings and Their Modules, Section 2.1: Direct Products and Direct Sums. I have a question regarding the proof of Proposition 2.1.1 Proposition 2.1.1 and its proof (together with with a relevant preliminary definition) read as follows...

I am reading Paul E. Bland's book, Rings and Their Modules. In Section 2.1: Direct Products and Direct Sums, Bland defines the direct product of a family of modules. He then, in Proposition 2.1.1 shows that there is a unique module homomorphism (or R-Linear mapping) from any particular R-module...

Hi everyone, :) Here's another question that I am struggling to complete. If you have any hints or suggestions for this one, I would be so grateful. :) Question: Let $S\subseteq R$ be rings and assume that $R_S$ is a finitely generated $S$-module. If $S$ is Artinian prove that $R$ is also...

Hi everyone, :) Want to confirm my understanding about Free and Finitely Generated modules. I want to know whether the following ideas are correct. Thank you for all your help. :) 1) Is every free module a finitely generated module? No. Because a free module may have an infinite basis. So we...

Hi, Guys I have a B78476A8135A003 Magnetic Module from EPCOS and I want to add a surge protector either on the TJ45 connector side or the Ethernet PHY side. I can't decide which way is more beneficial. Here is the topology: Ethernet PHY : B78476A8135A003 : Surge Protector (SLVU2.8-4) ...

Hi! I require help in writing a code where I want to put FUNCTION definitions in one module and INTERFACEs to the functions (as I use assumed-shape arrays in the functions) in another. But I get multiple errors when trying to compile. Could anyone assist me in solving this problem? Please see...

I was wondering if anyone would have an opinion on which four of the following final year Physics modules would be most useful to have completed post-graduation? Solid State Physics Atomic and Molecular Physics Physics in Medicine Nuclear and Fundamental Particle Physics Electromagnetic...

I am reading John Dauns book "Modules and Rings". I am having problems understanding the notation of Section 1-2 Direct Products and Sums (pages 5-6) - see attachment). In section 1-2.1 Dauns writes: ================================================== ====== "1-2.1 For any arbitrary...

I am reading John Dauns book "Modules and Rings". I am having problems understanding the notation in section 1-2 (see attachment) My issue is understanding the notation on Section 1-2, subsection 1-2.1 (see attachment). Dauns is dealing with the product \Pi \{ M_i | i \in I \} \equiv \Pi M_i...

Let R be a commutative ring and I, J be ideals of R. Show that (I + J)/J is isomorphic to I(R/J) as R modules. I am having trouble coming up with the explicit isomorphism. For I(R/J) I know any element can be expressed as i(r + J) = ir + J by definition of the action of R on R/J. As for (I +...

Hi, I'm wondering if anyone could suggest which out of the two below universities would give me the "better" mathematics major. By better I mean the most rigorous, the hardest and the one which will prepare me most for a phd. 1. http://www.ucl.ac.uk/maths/courses/undergraduates/ I won't be...

Dear all, I have an urgent task of finding the right experimental modules for Power Electronics Course in my university, for undergrad. level. Could you please provide me with a list of good and reliable vendors who can provide me with modules that can enable the students to perform...

Hi, I wanted to see what people think about my current viewpoint on recognizing structures in abstract algebra. You count the number of sets, and the number of operations for each set. You can also think about action by scalar or basis vectors. So monoids groups and rings have one set...

Hello, thank you for taking a look at this thread. Here is my dilemma, I can chose 30 credits from various math and physics courses (each worth 10) for my second year, but I've decided to do maths as the rest of my modules are all physics but there are so many I have no idea what maths modules...

I'm reading about tensor product of modules, there's a theorem in the book that leaves parts of the proof to the reader. I've attached the file, I didn't put this in HW section because first of all I thought this question was more advanced to be posted in there and also because I want to discuss...

Hey, these are the modules I have to choose for next year, still subject to change, so the available modules might not be the same when the form has to be in, but whatever. I want to specialise in things like General Rel, black holes, space time, etc... I can choose 6 from the following...

Hi guys, Basically I'm playing around with modules at the moment, and I can't work out why we can't have the group of integers as an F-module (F a field), where the left action is the identity. i.e F x Z ----> Z where we have f.z = z f in F, z in Z If this were possible, then Z would be a...

Dear Experts Does anyone know how big can we extend the gap between the 2 plates? Thanks. Regards Ramone

Hi, I keep seeing indirect uses of a result which I think would be stated as follows: If a module M over the unital associative algebra A is written M\cong S_1\oplus\cdots\oplus S_r (where the S_i are simple modules), then in any comosition series of M, the composition factors are, up to...

There is a Theorem that says FG-Modules are equivalent to group representations: "(1) If \rho is a representation of G over F and V = F^{n}, then V becomes an FG-Module if we define multiplication vg by: vg = v(g\rho), for all v in V, g in G. (2) If V is an FG-Module and B a basis of V...

Dear Sir,Madam,Friends 1)I did well in Number theory and found it easy. will " combinatorics" module be easy for me? 2) I have not put any time into studying Statistics & even did not bother to pass intro to Stat module. will Actuarial maths be easy for me ? does actuarial maths have a lot...

I have written many verilog codes and I need to make all of them in a single module. Can anyone help me?

I do not know if this is a common/standard construction, so here is my motivation for this question. From http://arxiv.org/abs/1002.1709" page 29: Is there a word for when there is such a one-to-one correspondence?

Homework Statement Let R be a commutative ring, and let F = R^{\oplus B} be a free R-module over R. Let m be a maximal ideal of R and take k = R/m to be the quotient field. Show that F/mF \cong k^{\oplus B} as k-vector spaces. The Attempt at a Solution If we remove the F and k...

I'm reading up on the classification of finitely generated modules over principal ideal domains. In doing so, I continuously come up on the statement "Let M be a finitely generated, free R-module." My question is, is this statement redundant? It seems to me that all finitely generated R-modules...

Homework Statement Let k be a field and k[x] be the set of polynomials over that field. Given that M is a module with presentation \begin{pmatrix} 1+ 3x & 2x & 3x \\ 1 + 2x & 1+ 2x -x^2 & 2x \\ x & x^2 & x \end{pmatrix} determine M. Homework Equations One can apply elementary row and...

Hi, All: I have seen Orthogonal groups defined in relation to a pair (V,q) , where V is a vector space , and q is a symmetric, bilinear quadratic form. The orthogonal group associated with (V,q) is then the subgroup of GL(V) (invertible linear maps L:V-->V ), i.e., invertible matrices...

Right so I'm a math major but what I really want to be is a theoretical physicist. 3rd and 4th year is when everything gets very specified, and I'm wondering which of the following modules would be most useful for that path? Here are the modules. Only 6 can be chosen from each term...

Homework Statement Let R be a ring with no zero divisors such that for any r,s\in R, there exist a,b \in R such that ar+bs=0. Prove: R=K \oplus L implies K=0 or L=0. Homework Equations Definition of direct sum of modules, integral domain... The Attempt at a Solution I didn't know...

hello! Hope you all will be at quiet ease. I am looking for the guidance to observe the performance analysis of MPPT (Maximum power point Tracker) in parallel and series configuration with similar solar modules. I have two solar modules each having the following rating: - Maximum power...

Let R be a discrete valuation ring with fraction field F. I believe it's straightforward to show that any torsion-free module M with the property that M \otimes_R F is a finite dimensional F-vector space is of the form R^m \oplus F^n. What if M \otimes_R F is infinite dimensional?

In atiyah's book on commutative algebra page 106 it says that elements in graded modules can be written uniquely as a sum of homogeneous elements. More precisely: If A = \oplus^{\infty}_{n=0} A_n is a graded ring, and M = \oplus^{\infty}_{n=0} M_n is a graded A-module, then an element y \in...

Hi, I want to couple two different modules of COMSOL. For example u is the solution of Module 1 and I want to give 0.95*u+a as subdomain settings parameter in module 2. Here a is a vector. I have succeeded with u and 0.95*u to use as subdomain settings parameter of module 2 but when I add a ...

Choosing modules for theoretical Physics from Math Graduate Diploma course: Hi forum members, I am studying Math Graduate Diploma at Kings College london. I am going to do M.Sc Theoretical Physics next year. I need your advice in choosing Math Grad Diploma modules closely related to the...

Can you please suggest me some books to read on this topic? It's for my final year project! I would much appreciate it!

Hello! I'm currently taking a course in group- and ring theory, and we are now dealing with a chapter on finitely generated modules over PIDs. I have stumbled across some problems that I can't really get my head around. It is one in particular that I would very much like to understand, and I...

Hello. I have to choose 2 of the above Mechanical Engineering modules and i would like to make the best choice for future jobs and better CV. 1. Engineering Materials 2. Resource Management 3. Automated Manufacturing 4. Power Hydraulics Any help? Cheers

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...

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...

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...

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...

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...

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.

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