Matches in SemOpenAlex for { <https://semopenalex.org/work/W4290607218> ?p ?o ?g. }
Showing items 1 to 71 of
71
with 100 items per page.
- W4290607218 abstract "In this paper we study initial topological properties of the (non-)finitely-generated locus of Frobenius Algebra coming from Stanley-Reisner rings defined through face ideals. More specifically, we will give a partial answer to a conjecture made by M. Katzman about the openness of the finitely generated locus of such Frobenius algebras. This conjecture can be formulated in a precise manner: Let us define begin{equation*} U={Pin text{Spec}(R)~:~mathcal{F}(E_{R_{p}})~text{is a finitely generated}~R_{p}text{-algebra}} end{equation*} where $mathcal{F}$ denotes the Frobenius functor and $E_{R_{p}}$ the injective hull of the residual field of the local ring $(R_{p},pR_{p})$. Is the locus $U$ an open set in the Zariski Topology? In the case where $R$ is a ring of the form $R=K[[x_{1},dots ,x_{n}]]/I,$ where $Isubset R$ is a face ideal, i.e., square-free monomial ideal, we show that the corresponding $U$ has non-empty interior. Even more, we prove that in general $U$ contains two different types of opens sets and that in specific situation its complement contains intersections of opens and closes sets in the Zariski topology. Furthermore, we explicitly verify in some non-trivial examples that $U$ is an non-trivial open set." @default.
- W4290607218 created "2022-08-08" @default.
- W4290607218 creator A5008092153 @default.
- W4290607218 creator A5039796966 @default.
- W4290607218 creator A5060002605 @default.
- W4290607218 creator A5076583109 @default.
- W4290607218 creator A5078893628 @default.
- W4290607218 date "2021-05-11" @default.
- W4290607218 modified "2023-09-27" @default.
- W4290607218 title "On the Topological Structure of the (Non-) Finitely-generated Locus of Frobenius Algebras emerging from Stanley-Reisner Rings" @default.
- W4290607218 doi "https://doi.org/10.48550/arxiv.2105.04782" @default.
- W4290607218 hasPublicationYear "2021" @default.
- W4290607218 type Work @default.
- W4290607218 citedByCount "0" @default.
- W4290607218 crossrefType "posted-content" @default.
- W4290607218 hasAuthorship W4290607218A5008092153 @default.
- W4290607218 hasAuthorship W4290607218A5039796966 @default.
- W4290607218 hasAuthorship W4290607218A5060002605 @default.
- W4290607218 hasAuthorship W4290607218A5076583109 @default.
- W4290607218 hasAuthorship W4290607218A5078893628 @default.
- W4290607218 hasBestOaLocation W42906072181 @default.
- W4290607218 hasConcept C104317684 @default.
- W4290607218 hasConcept C11252640 @default.
- W4290607218 hasConcept C114614502 @default.
- W4290607218 hasConcept C118615104 @default.
- W4290607218 hasConcept C128107574 @default.
- W4290607218 hasConcept C136119220 @default.
- W4290607218 hasConcept C14394260 @default.
- W4290607218 hasConcept C156772000 @default.
- W4290607218 hasConcept C162860070 @default.
- W4290607218 hasConcept C180950851 @default.
- W4290607218 hasConcept C184720557 @default.
- W4290607218 hasConcept C185592680 @default.
- W4290607218 hasConcept C202444582 @default.
- W4290607218 hasConcept C2780990831 @default.
- W4290607218 hasConcept C33923547 @default.
- W4290607218 hasConcept C55493867 @default.
- W4290607218 hasConcept C84597430 @default.
- W4290607218 hasConceptScore W4290607218C104317684 @default.
- W4290607218 hasConceptScore W4290607218C11252640 @default.
- W4290607218 hasConceptScore W4290607218C114614502 @default.
- W4290607218 hasConceptScore W4290607218C118615104 @default.
- W4290607218 hasConceptScore W4290607218C128107574 @default.
- W4290607218 hasConceptScore W4290607218C136119220 @default.
- W4290607218 hasConceptScore W4290607218C14394260 @default.
- W4290607218 hasConceptScore W4290607218C156772000 @default.
- W4290607218 hasConceptScore W4290607218C162860070 @default.
- W4290607218 hasConceptScore W4290607218C180950851 @default.
- W4290607218 hasConceptScore W4290607218C184720557 @default.
- W4290607218 hasConceptScore W4290607218C185592680 @default.
- W4290607218 hasConceptScore W4290607218C202444582 @default.
- W4290607218 hasConceptScore W4290607218C2780990831 @default.
- W4290607218 hasConceptScore W4290607218C33923547 @default.
- W4290607218 hasConceptScore W4290607218C55493867 @default.
- W4290607218 hasConceptScore W4290607218C84597430 @default.
- W4290607218 hasLocation W42906072181 @default.
- W4290607218 hasOpenAccess W4290607218 @default.
- W4290607218 hasPrimaryLocation W42906072181 @default.
- W4290607218 hasRelatedWork W1932628765 @default.
- W4290607218 hasRelatedWork W2029736304 @default.
- W4290607218 hasRelatedWork W2046286811 @default.
- W4290607218 hasRelatedWork W2066643928 @default.
- W4290607218 hasRelatedWork W2079663516 @default.
- W4290607218 hasRelatedWork W2120384785 @default.
- W4290607218 hasRelatedWork W2619453705 @default.
- W4290607218 hasRelatedWork W2963168043 @default.
- W4290607218 hasRelatedWork W3092283481 @default.
- W4290607218 hasRelatedWork W3161434874 @default.
- W4290607218 isParatext "false" @default.
- W4290607218 isRetracted "false" @default.
- W4290607218 workType "article" @default.