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Jul
28
awarded  Popular Question
Jul
25
comment Finitely generated projective module
I was wondering why $N$ is finitely generated... I was thinking about this for more than a day.... Now i got it, direct summand of a finitely generated module is finitely generated and that is why $N$ is finitely generated... I thought i should write that here so it may be of use to some one...
Jul
24
awarded  Yearling
Jul
24
comment $I\otimes I$ is torsion free for a principal ideal $I$ in domain $R$
I have realized this after darij grinberg has given that hint... Thanks anyways...
Jul
24
accepted $I\otimes I$ is torsion free for a principal ideal $I$ in domain $R$
Jul
23
comment $I\otimes I$ is torsion free for a principal ideal $I$ in domain $R$
@user26857: i could have said $\varphi: I\times I\rightarrow R$ with same map as in the question.. That should not be an issue.. right?
Jul
23
comment $I\otimes I$ is torsion free for a principal ideal $I$ in domain $R$
@user26857 : :D sorry, now i understand my mistake... I guess $\varphi(xa,ya)=xya$ works... Every elemnt in $I\otimes I$ is a simple tensor... $a_1\otimes b_1+\cdots+ a_n\otimes b_n=r_1a\otimes s_1a+\cdots+r_na\otimes s_na=(r_1s_1+\cdots+s_ns_n)(a\otimes a)$
Jul
23
comment $I\otimes I$ is torsion free for a principal ideal $I$ in domain $R$
@user26857 : I thought this was better choice.. I am wrong... Can you give some hint..
Jul
23
comment $I\otimes I$ is torsion free for a principal ideal $I$ in domain $R$
Oh Oh oh..... So, $I\cong_R R$ so, $I\otimes_R I\cong_R\otimes_R R=R$.. Thus, $I\otimes_R I \cong_R$. As $R$ is torsion free as $R$ module, then so is $I\otimes I$?? @darijgrinberg
Jul
23
asked $I\otimes I$ is torsion free for a principal ideal $I$ in domain $R$
Jun
20
awarded  Popular Question
Jun
16
comment Let $X,Y$ be metric spaces , $f : X \rightarrow Y$ be a continuous function , $A$ be a bounded subset of $X$ and let $B =f(A)$.
$f:(0,1]\rightarrow \mathbb{R}$ with $f(x)=\frac{1}{x}$??
Jun
5
comment Is it bad to keep aside Lang's Algebra in graduate school?
@Mathemagician1234 : It is IIT :)
Jun
4
comment Characteristic polynomial of a complex 4 by 4 matrix
you tried something?
Jun
3
comment Evaluate $\lim\limits_{x\to\infty}(\sin\sqrt{x+1}-\sin\sqrt{x})$
Do you know when can you write $\lim(a_n-b_n)=\lim a_n-\lim b_n$?
Jun
2
reviewed Leave Open Showing that $\sin'(x)=\cos(x)$
Jun
2
accepted Noetherian ring under some conditions has at least two minimal prime ideals
Jun
1
comment The number of $2$-Sylow subgroups in $S_4 \times S_3$
$p$ divides $9$. So, $p=0$ or $p=4$... WHat do you mean by that?
Jun
1
revised Noetherian ring under some conditions has at least two minimal prime ideals
added 798 characters in body
May
31
comment Noetherian ring under some conditions has at least two minimal prime ideals
Noetherian assumption is superflous but as it was asking to use previous exercise in whihc there was a decomposition for ideal $(0)$ noetherian condition was imposed just to make sure that some primary decomposition of ideal $(0)$ exists....