Separable categories
type: Item
instance of: scholarly article
title: Separable categories
zbMATH Open document ID: 0581.18005
DOI: 10.1016/0022-4049(86)90026-5
author: Steven M. Amgott
published in: Journal of Pure and Applied Algebra
publication date: 1986-01-01T00:00:00Z
review text: This paper develops the extension of ring theory to the theory of small additive categories (here called ringoids). Monoid rings are generalized to free additive categories \({\mathbb{Z}}C\) on categories C. The question of separability of \({\mathbb{Z}}C\) is characterized in terms of C. This allows the author to prove a conjecture of \textit{B. Mitchell} [Separable algebroids, Mem. Am. Math. Soc. 333 (1985)] that, for such a C, the category of \({\mathbb{Z}}C\)-modules is equivalent to the product of copies of the category of abelian groups.
Mathematics Subject Classification ID: 18E05
Mathematics Subject Classification ID: 16H05
zbMATH DE Number: 3929243
zbMATH Keywords: separarable algebra
zbMATH Keywords: monoid rings
zbMATH Keywords: Morita equivalence
zbMATH Keywords: idempotent completion
zbMATH Keywords: small additive categories
zbMATH Keywords: ringoids
reviewed by: Ross H. Street
MaRDI profile type: Publication
full work available at URL: 0022-4049(86)90026-5
OpenAlex ID: W4210382223
cites work: Separable semigroup algebras
cites work: Q3848243
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cites work: A note on separable integral semigroup rings
description: scientific article; zbMATH DE number 3929243