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arXiv · 2302.01868

Identities and derived lengths of finitary incidence algebras and their group of units

Mykola Khrypchenko·Salvatore Siciliano
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Abstract

Let $FI(X,K)$ be the finitary incidence algebra of a poset $X$ over a field $K$. In this short note we establish when $FI(X,K)$ satisfies a polynomial identity and when its group of units $\mathcal{U}(FI(X,K))$ satisfies a group identity. The Lie derived length of $FI(X,K)$ and the derived length of $\mathcal{U}(FI(X,K))$ are also determined.

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Mykola Khrypchenko, Salvatore Siciliano. 2023-02-03. Identities and derived lengths of finitary incidence algebras and their group of units. https://arxiv.org/abs/2302.01868

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