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Research Article | Open Access

On the decomposition of perfect arbitrary algebras as a direct sum of indecomposable ideals

Department of Mathematics, Faculty of Sciences, University of Cádiz, Campus de Puerto Real, 11510, Puerto Real, Cádiz, Spain
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Abstract

We consider perfect algebras A (that is, A 2 = A), in their greatest generality. That is, of arbitrary dimension, over an arbitrary base field, and no identity or condition are assumed for the product. We introduce a certain action involving the linear group of A and provide a characterization and a necessary condition for A, in terms of the above action, to be a direct sum of indecomposable ideals.

Keywords

arbitrary algebradecompositionindecomposable idealperfect algebralinear groupstructure theory
CLC number: 15A21, 17A01, 17A60

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AIMS Mathematics
Volume 11 Issue 5,
May 2026
Pages 14840-14856
DOI: 10.3934/math.2026611

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Martín AJC. On the decomposition of perfect arbitrary algebras as a direct sum of indecomposable ideals. AIMS Mathematics, 2026, 11(5): 14840-14856. https://doi.org/10.3934/math.2026611

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Received: 04 March 2026
Revised: 13 May 2026
Accepted: 19 May 2026
Published: 15 May 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)