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2 votes
0 answers
123 views

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,...
Sylvain JULIEN's user avatar
5 votes
1 answer
759 views

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 ...
Chris 's user avatar
  • 303
4 votes
1 answer
316 views

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 ...
Aurélien Djament's user avatar
5 votes
0 answers
337 views

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 $I(\cap_{k=1}^{\infty}I^k M)=\cap_{k=1}^{\infty}I^k M$ . ...
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4 votes
0 answers
280 views

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 ...
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