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 Yearling
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Apr
21
revised Problems with understanding the proof of noetherian ring
added 939 characters in body
Apr
21
answered Problems with understanding the proof of noetherian ring
Apr
21
revised Some theorems in euclidean geometry have incomplete proofs
Removing tags that don't fit
Apr
21
comment Is the zero ideal $\{0_{M_2(\mathbb{R})}\}$ maximal in $M_{2}(\mathbb{R})$?
@Jellyfish : $M_2(\Bbb R)$ is not a division ring.
Apr
20
comment Bourbaki Algebra Chapter IV - Exercise 9(b)
By forcing readers to go find this book, you are screening out most of the audience capable of helping you. Even if someone has that book and wants to help you, maybe they can't be bothered to look up the whole problem for you. You have it right there, just write it down...
Apr
20
revised Characteristic of a Finite Integral Domain
added 513 characters in body
Apr
20
answered Characteristic of a Finite Integral Domain
Apr
20
comment Prove $Rm$ simple $\iff Ann(m)$ is a left ideal of $R$.
@123 of course it does: we are applying the correspondence theorem for modules, not rings. If K is a left ideal or two sided ideal, the left module R/K does not care a bit if K is also a right module or not.
Apr
18
comment Rentschler's theorem on non-commutative algebras
To say something about the Weyl algebras, you would need a stronger conclusion dealing with quotients of free algebras.
Apr
17
awarded  Yearling
Apr
17
revised If C is a chain of non-principal ideals and the union of the ideals of the chain contains a generator, why is the union then principal
deleted 23 characters in body
Apr
17
comment Proving that a Left semisimple ring $R$ is both left noetherian and left artinian
An infinite direct sum of (nonzero) $R$-modules is not finitely generated, and $R_R$ is finitely generated. It only takes an application of modus tollens to conclude that $R$ is not an infinite direct sum of nonzero modules.
Apr
17
comment Proving that a Left semisimple ring $R$ is both left noetherian and left artinian
@Prayagdeep No, this is a direct proof, and there is no proof by contradiction here. By showing the last line, egreg has established that the two direct sums are equal, and it follows that $\Lambda=\Lambda_0$.
Apr
17
answered If C is a chain of non-principal ideals and the union of the ideals of the chain contains a generator, why is the union then principal
Apr
17
comment How is this map a well-defined homomorphism?
@sara I can't see where you are getting that from. Can you be specific about what you are reading?
Apr
17
comment Verification: Let $R$ be a unique factorization domain and let $a,b \in R$ be nonzero, non-unit elements. Prove that $a$ and $b$ have a LCM
This is a question and answer site. Do you have a question?
Apr
15
revised In Ring Theory, does a 'power' of a morphism represent composition?
added 13 characters in body
Apr
15
comment In Ring Theory, does a 'power' of a morphism represent composition?
@ZhenLin Yeah, right, I guess I had continuous linear functions in mind.
Apr
15
comment Property of free submodules for a module over a PID
Dear @JyrkiLahtonen: The example at the link above is a sum of two free cyclic modules which isn't free, so finite generation does not help, here. The issue is that the sum of torsion-free submodules need not be torsion-free. Regards
Apr
15
comment Property of free submodules for a module over a PID
@user74230 : please consider writing your solution as a solution.