User student - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T05:14:08Z http://mathoverflow.net/feeds/user/17545 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/89547/example-reduced-and-divisible-modules example reduced and divisible modules student 2012-02-26T03:06:58Z 2012-02-26T03:06:58Z <p>in article <a href="http://mathoverflow.net/questions/89406/example-of-reduced-modules" rel="nofollow">http://mathoverflow.net/questions/89406/example-of-reduced-modules</a></p> <p>Chris Leary asked me yesterday that: $A=Z_n$ is torsion and $C=Z$ is tosion free. What can you say about $Hom(A,C)$ in this case? With the same C and A=Q, a divisible abelian group, what can you say about Hom(A,C)? </p> <p>How can you show me an homomorphism non-trival from $Z_n$ to $Z$? suggest that you contruct as:</p> <p>$f(x+nZ)=x$. clearly $f$ is not map!</p> <p>i really hope your answer! </p> http://mathoverflow.net/questions/76522/reduced-module-over-integral-domain reduced module over integral domain student 2011-09-27T15:09:05Z 2011-09-28T08:27:55Z <p>hi, all! I want to know what is the definition of reduced module voer integral domain. I search in Google but i am confused for different definitions. Thanhk you very much!</p> http://mathoverflow.net/questions/76522/reduced-module-over-integral-domain/76614#76614 Answer by student for reduced module over integral domain student 2011-09-28T08:27:55Z 2011-09-28T08:27:55Z <p>definition in your document defined reduced module over general ring, i want to know what is definition of a reduced module over integral domain (because definition of torsion-free modules over general ring and definition of them in integral domain are different). Now, i have some definitions: 1) a module is called reduced iff i have only injective modules 0. 2) a module $C$ is called reduced iff $Hom(A,C)=0$ for all divisible module $C$.</p> <p>I do not know which definition for module over integral domain or none of them? are they equivalent iff $R$ is integral domain?</p> <p>Thank you very much, good luck to you!</p> http://mathoverflow.net/questions/76613/weak-divisble-module weak divisble module student 2011-09-28T08:12:15Z 2011-09-28T08:12:15Z <p>hi, all! I want to know what is the definition of reduced module over general ring. </p> <p>I remember that: a module $B$ always have smallest submodule $D(B)$ satisfy $B/D(B)$ is divisible module. If $D(B)=B$ then $B$ is called weak divisible module". Is it exactly? if exact, how can we infer that a weak divisible module always is a divisible module?</p> <p>Thanhk you very much!</p> http://mathoverflow.net/questions/76522/reduced-module-over-integral-domain/76612#76612 Answer by student for reduced module over integral domain student 2011-09-28T08:03:51Z 2011-09-28T08:03:51Z <p>thank you very much, i is document i need. good luck to you</p> http://mathoverflow.net/questions/75412/torsion-product torsion product student 2011-09-14T15:27:33Z 2011-09-14T16:48:22Z <p>Let $R=R_1 \oplus ... \oplus R_r$; $A$ and $B$ are $R$-modules. We know that $A=A_1 \oplus ... \oplus A_r$, $B=B_1 \oplus ... \oplus B_r$ with $A_i = R_i.A$, $B_i = R_i.B$. Now i have not find following fomula yet: <code>$$\mathrm{Tor}_n^R (A,B) \cong \sum \mathrm{Tor}_n^{R_i}(A_i, B_i); \quad \mathrm{Ext}_R^n (A,B) \cong \sum \mathrm{Ext}_{R_i}^n (A_i, B_i)$$</code> Please show me which document should i read or help me prove these formula. Thanks!</p> http://mathoverflow.net/questions/74654/torsion-free-modules-over-general-ring/75102#75102 Answer by student for torsion free modules over general ring student 2011-09-10T14:09:02Z 2011-09-10T14:09:02Z <p>thank for your all answers! Here is my ideas: How can i prove the following proposition: " If every finitely generated ideal of R is principal, then a torsion - free R-module is flat"</p> <p>Because most of books i have prove this property when R is integral domain, while i want to know how can we prove when R is general ring.</p> http://mathoverflow.net/questions/74654/torsion-free-modules-over-general-ring torsion free modules over general ring student 2011-09-06T14:27:08Z 2011-09-10T14:09:02Z <p>i want to know how to prove a torsion free modules over general ring is flat. (in "lecture on ring and modules, T.Y.Lam prove in case R is interal domain). please help me prove it or give me some books or article concern this problem. Thanks! </p> http://mathoverflow.net/questions/74337/torsion-free-modules torsion-free modules student 2011-09-02T09:38:23Z 2011-09-02T10:37:53Z <p>Let R is a PP-ring. we know that any submodule of a torsion-free left R-module is torsion-free; a direct sum of a torsion-free left R-modules is torsion-free.</p> <p>I do not know the reason of following conclusion: "Since $l(\lambda )$ is finitely generated when principle left ideal $R \lambda$ is projective, we have every right R-module possesses the largest torsion-free factor module".</p> <p>Here, $l(\lambda)= \left\lbrace r \in R; \lambda r = 0\right\rbrace$</p> <p>Please help me explain it clearly! Thank you very much!</p> http://mathoverflow.net/questions/74336/equivalence-of-flat-modules equivalence of Flat modules student 2011-09-02T09:33:29Z 2011-09-02T09:33:29Z <p>Hi, All. I need to solve following exercise but i can not. Please help me solve it.</p> <p>Exercise. For each R-module A establish the equivalence of the following conditions: (a) A is R-flat. (b) $Tor_1^R (A, R/I)$ for each left ideal I of R.</p> <p>Thank you very much. I really appreciate your idea!</p> http://mathoverflow.net/questions/74654/torsion-free-modules-over-general-ring/75102#75102 Comment by student student 2011-09-16T09:25:24Z 2011-09-16T09:25:24Z thank you very much. let me try to prove http://mathoverflow.net/questions/75412/torsion-product Comment by student student 2011-09-16T09:24:06Z 2011-09-16T09:24:06Z thank for everyone. I try to prove it now!