All Questions
Tagged with ideals noetherian
5 questions
2
votes
0
answers
123
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Quasi-ideals and Erdős conjecture on arithmetic progressions
Starting to read a book about algebraic geometry as well as the Wikipedia article on Erdős conjecture on arithmetic progressions, I came to think of what follows.
Let $A$ be a set of positive integers,...
5
votes
1
answer
759
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On the annihilator of a module
Question. Let $A$ be a Noetherian ring and $M$ a finitely generated $A$-module. Does there always exist an element $s\in M$ such
that $\mathrm{Ann}(s)=\mathrm{Ann}(M)$?
Remark. The annihilator of a ...
4
votes
1
answer
316
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Noetherian ring with a "strange" idempotent ideal
Do you know a left-noetherian ring $R$ with a two-sided ideal $I$ such that:
$I=I.I$;
$I$ is not projective as a left $R$-module (and better, the tensor product over $R$ of $I$ with itself is not a ...
5
votes
0
answers
337
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Can the Artin-Rees lemma be derived from Krull Intersection theorem?
The Krull Intersection theorem states that : For a finitely generated module $M$ over a Noetherian ring $R$ and any ideal $I$ of $R$, we have $I(\cap_{k=1}^{\infty}I^k M)=\cap_{k=1}^{\infty}I^k M$ . ...
4
votes
0
answers
280
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Noetherian rings as homomorphic image of finite direct product of Noetherian domains?
A theorem of Hungerford says that : Every PIR (principal ideal ring , obviously commutative ) is a homomorphic image of a finite direct product of PID s . My question is , is there a similar criteria ...