On Koszulity of Finite Posets

2016/05/18 by Adrian Manea, Manea, Adrian, Dragoş Ştefan +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #K-Theory and Homology (math.KT) #Primary 16E40 #Secondary 16T15

paper · pdf · doi:10.48550/arxiv.1605.05458

openalex publication_date 2016/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove in a unifying way several equivalent descriptions of Koszul rings, some of which being well known in the literature. Most of them are stated in terms of coring theoretical properties of \Tor_n^A(R,R). As an application of these characterizations we investigate the Koszulity of the incidence rings for finite graded posets. Based on these results, we describe an algorithm to produce new classes of Koszul posets (i.e. graded posets whose incidence rings are Koszul). Specific examples of Koszul posets are included.

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