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Results tagged with ra.rings-and-algebras
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user 338309
Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
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When nilradical belongs to a Gabriel filter
Recall that a Gabriel filter of ideals $\mathscr{I}_\sigma$ of a commutative ring $R$ is a non–empty filter of ideals satisfying that every ideal
$I$ of $R$, for which there exists an ideal $J\in\math …
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An example of a commutative ring with a non-zero nil ideal that is idempotent
Recall that an ideal of a commutative ring is said to be a nil ideal if each of its elements is nilpotent. I am looking for a non-zero nil ideal of a commutative ring that is idempotent.
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The existence of two maximal ideals with the same set of idempotents
Let $R$ be a commutative ring with identity and $A$ and $B$ be two proper ideals of $R$ such that $A+B=R$ and for each $r^2=r\in R$ we have either $r\not\in A$ or $r-1\not\in B$. How can we prove the …
- 147
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An example of a local integral domain with special spectrum
I am looking for a local integral domain $(D, m)$ with $Spec(D)=\{0,m\}\cup\{ P_i\}_i$ such that $P_i's$ are incomparable (that is, $P_i\not\subseteq P_j$ and $P_j\not\subseteq P_i$ for $i\not= j$) …
- 147
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Finding an injective envelope containing another injective envelope
Let $R$ be a local principal ideal domain (PID) with only two prime ideals $0$ and $P$, and let $M$ be an $R$-module. Let for $r\in R$ and $m\in M$, $rm\not=0$. Now if $E(rm)$ is a fixed injective env …
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