{"title":"Isomorphisms and derivations of partial flag incidence algebras","authors":"M. Khrypchenko","doi":"10.1142/s0218196722500084","DOIUrl":null,"url":null,"abstract":"Let [Formula: see text] and [Formula: see text] be finite posets and [Formula: see text] a commutative unital ring. In the case where [Formula: see text] is indecomposable, we prove that the [Formula: see text]-linear isomorphisms between partial flag incidence algebras [Formula: see text] and [Formula: see text] are exactly those induced by poset isomorphisms between [Formula: see text] and [Formula: see text]. We also show that the [Formula: see text]-linear derivations of [Formula: see text] are trivial.","PeriodicalId":13615,"journal":{"name":"Int. J. Algebra Comput.","volume":"05 1","pages":"193-209"},"PeriodicalIF":0.0000,"publicationDate":"2021-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Algebra Comput.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218196722500084","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
Let [Formula: see text] and [Formula: see text] be finite posets and [Formula: see text] a commutative unital ring. In the case where [Formula: see text] is indecomposable, we prove that the [Formula: see text]-linear isomorphisms between partial flag incidence algebras [Formula: see text] and [Formula: see text] are exactly those induced by poset isomorphisms between [Formula: see text] and [Formula: see text]. We also show that the [Formula: see text]-linear derivations of [Formula: see text] are trivial.
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