Skew incidence rings and the isomorphism problem

2021/04/14 by Érica Z. Fornaroli, Fornaroli, Érica Zancanella
Computer Science · Mathematics · #16N20 #16S60 #16U70 #16U99 #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Primary 16S50 #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #Secondary 16U60

paper · pdf · doi:10.48550/arxiv.2104.06796

openalex publication_date 2021/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a finite partially ordered set, R an associative unital ring and σ an endomorphism of R. We describe some properties of the skew incidence ring I(X,R,σ) such as invertible elements, idempotents, the Jacobson radical and the center. Moreover, if the skew incidence rings I(X,R,σ) and I(Y,S,τ) are isomorphic and the only idempotents of R,S are the trivial ones, we show that the partially ordered sets X and Y are isomorphic.

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