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Results tagged with ac.commutative-algebra
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user 143705
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
4
votes
1
answer
361
views
A local ring with a unique minimal ideal
Let $R$ be a commutative ring with 1 such that it is local with a unique non-idempotent minimal ideal, that is, there are two ideals $I$ and $m$ of $R$ such that for each ideal $K$ of $R$ with $0\not= …
- 42.9k
4
votes
1
answer
143
views
Annihilators and principal ideals: a characterization for a property of an element
Let $R$ be a commutative ring with identity and $a\in R$ has the property that for $b\in R$ if $\langle a\rangle\cap\langle b\rangle=\{0\}$, then $ann_R(a)+ann_R(b)=R$, where $ann_R(x) :=\{r\in R\mid …
- 18.7k