Canonical solution of universal problem for the prolongation of algebra
by a local algebra
Bienvenu Roland Bassiloua\,^1 and Norbert Mahoungou Moukala\,^2
\,^{1} Département de Mathématiques, Faculté des Sciences et Techniques, Université Marien Ngouabi, B.P69, Brazzaville, Congo.
\,^{2} Département des Sciences Exactes, Ecole Normale Supérieure, Université Marien Ngouabi, B.P69, Brazzaville, Congo.
Pages 26-42 | Received 03 November 2024, Accepted 10 June 2025, Published 17 July 2026
Abstract
In this paper, we introduce the notion of prolongations of algebras by a local algebra. We propose a universal problem for the prolongations of algebras by a local algebra and we describe the existence and uniqueness of the solution of this problem. We provide several propositions which illustrate the properties of functors in the category of prolongations of algebra by a local algebra.
Keywords: Prolongation of algebra, symmetric algebra, local algebra, categories of algebras.
MSC numbers: Primary 13B02, 16S10; Secondary 16P10, 08C05.
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