Local Derivations of Finitary Incidence Algebras

Mykola Khrypchenko

Local Derivations of Finitary Incidence Algebras

Rings and Algebras 2017-07-13 v2

Authors: Mykola Khrypchenko

Abstract

Let $P$ be a partially ordered set, $R$ a commutative ring with identity and $FI(P,R)$ the finitary incidence algebra of $P$ over $R$ . In this note we prove that each $R$ -linear local derivation of $FI(P,R)$ is a derivation, which partially generalizes a result by Nowicki and Nowosad.

Keywords

finitary incidence algebras local derivations partially ordered sets commutative rings derivations

Cite

@article{arxiv.1704.09016,
  title  = {Local Derivations of Finitary Incidence Algebras},
  author = {Mykola Khrypchenko},
  journal= {arXiv preprint arXiv:1704.09016},
  year   = {2017}
}

Comments

Minor corrections. In particular, the last steps of the proof of Lemma 2.1 were better clarified

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