Matches in SemOpenAlex for { <https://semopenalex.org/work/W4298303208> ?p ?o ?g. }
Showing items 1 to 84 of
84
with 100 items per page.
- W4298303208 abstract "Let $R$ be a (commutative Noetherian) local ring of prime characteristic that is $F$-pure. This paper studies a certain finite set ${mathcal I}$ of radical ideals of $R$ that is naturally defined by the injective envelope of the simple $R$-module. This set ${mathcal I}$ contains $0$ and $R$, and is closed under taking primary components. For a multiplicatively closed subset $S$ of $R$, the concept of tight closure with respect to $S$, or $S$-tight closure, is discussed, together with associated concepts of $S$-test element and $S$-test ideal. It is shown that an ideal of $R$ belongs to ${mathcal I}$ if and only if it is the $S'$-test ideal of $R$ for some multiplicatively closed subset $S'$ of $R$. When $R$ is complete, ${mathcal I}$ is also `closed under taking test ideals', in the following sense: for each proper ideal $C$ in ${mathcal I}$, it turns out that $R/C$ is again $F$-pure, and if $J$ and $K$ are the unique ideals of $R$ that contain $C$ and are such that $J/C$ is the (tight closure) test ideal of $R/C$ and $K/C$ is the big test ideal of $R/C$, then both $J$ and $K$ belong to ${mathcal I}$. The paper ends with several examples." @default.
- W4298303208 created "2022-10-02" @default.
- W4298303208 creator A5059667561 @default.
- W4298303208 date "2013-01-29" @default.
- W4298303208 modified "2023-10-16" @default.
- W4298303208 title "Tight closure with respect to a multiplicatively closed subset of an $F$-pure local ring" @default.
- W4298303208 doi "https://doi.org/10.48550/arxiv.1301.6890" @default.
- W4298303208 hasPublicationYear "2013" @default.
- W4298303208 type Work @default.
- W4298303208 citedByCount "0" @default.
- W4298303208 crossrefType "posted-content" @default.
- W4298303208 hasAuthorship W4298303208A5059667561 @default.
- W4298303208 hasBestOaLocation W42983032081 @default.
- W4298303208 hasConcept C111472728 @default.
- W4298303208 hasConcept C114614502 @default.
- W4298303208 hasConcept C118211362 @default.
- W4298303208 hasConcept C118615104 @default.
- W4298303208 hasConcept C124973616 @default.
- W4298303208 hasConcept C128107574 @default.
- W4298303208 hasConcept C136119220 @default.
- W4298303208 hasConcept C138885662 @default.
- W4298303208 hasConcept C142109727 @default.
- W4298303208 hasConcept C146834321 @default.
- W4298303208 hasConcept C156923205 @default.
- W4298303208 hasConcept C161491579 @default.
- W4298303208 hasConcept C162324750 @default.
- W4298303208 hasConcept C164953516 @default.
- W4298303208 hasConcept C170320730 @default.
- W4298303208 hasConcept C178790620 @default.
- W4298303208 hasConcept C183778304 @default.
- W4298303208 hasConcept C185592680 @default.
- W4298303208 hasConcept C202444582 @default.
- W4298303208 hasConcept C2776639384 @default.
- W4298303208 hasConcept C2777726979 @default.
- W4298303208 hasConcept C2779057376 @default.
- W4298303208 hasConcept C2780378348 @default.
- W4298303208 hasConcept C2780586882 @default.
- W4298303208 hasConcept C33923547 @default.
- W4298303208 hasConcept C34447519 @default.
- W4298303208 hasConcept C45804927 @default.
- W4298303208 hasConceptScore W4298303208C111472728 @default.
- W4298303208 hasConceptScore W4298303208C114614502 @default.
- W4298303208 hasConceptScore W4298303208C118211362 @default.
- W4298303208 hasConceptScore W4298303208C118615104 @default.
- W4298303208 hasConceptScore W4298303208C124973616 @default.
- W4298303208 hasConceptScore W4298303208C128107574 @default.
- W4298303208 hasConceptScore W4298303208C136119220 @default.
- W4298303208 hasConceptScore W4298303208C138885662 @default.
- W4298303208 hasConceptScore W4298303208C142109727 @default.
- W4298303208 hasConceptScore W4298303208C146834321 @default.
- W4298303208 hasConceptScore W4298303208C156923205 @default.
- W4298303208 hasConceptScore W4298303208C161491579 @default.
- W4298303208 hasConceptScore W4298303208C162324750 @default.
- W4298303208 hasConceptScore W4298303208C164953516 @default.
- W4298303208 hasConceptScore W4298303208C170320730 @default.
- W4298303208 hasConceptScore W4298303208C178790620 @default.
- W4298303208 hasConceptScore W4298303208C183778304 @default.
- W4298303208 hasConceptScore W4298303208C185592680 @default.
- W4298303208 hasConceptScore W4298303208C202444582 @default.
- W4298303208 hasConceptScore W4298303208C2776639384 @default.
- W4298303208 hasConceptScore W4298303208C2777726979 @default.
- W4298303208 hasConceptScore W4298303208C2779057376 @default.
- W4298303208 hasConceptScore W4298303208C2780378348 @default.
- W4298303208 hasConceptScore W4298303208C2780586882 @default.
- W4298303208 hasConceptScore W4298303208C33923547 @default.
- W4298303208 hasConceptScore W4298303208C34447519 @default.
- W4298303208 hasConceptScore W4298303208C45804927 @default.
- W4298303208 hasLocation W42983032081 @default.
- W4298303208 hasLocation W42983032082 @default.
- W4298303208 hasOpenAccess W4298303208 @default.
- W4298303208 hasPrimaryLocation W42983032081 @default.
- W4298303208 hasRelatedWork W1510183621 @default.
- W4298303208 hasRelatedWork W1985066958 @default.
- W4298303208 hasRelatedWork W1988864371 @default.
- W4298303208 hasRelatedWork W2029311697 @default.
- W4298303208 hasRelatedWork W2045656292 @default.
- W4298303208 hasRelatedWork W2085382051 @default.
- W4298303208 hasRelatedWork W2093055753 @default.
- W4298303208 hasRelatedWork W2321967812 @default.
- W4298303208 hasRelatedWork W2952732939 @default.
- W4298303208 hasRelatedWork W4298303208 @default.
- W4298303208 isParatext "false" @default.
- W4298303208 isRetracted "false" @default.
- W4298303208 workType "article" @default.