Опис алгебри Ауслендера єдиної некомутативної напівгрупи третього порядку з ненульовим нільпотентним елементом

One way to describe the category of representations over a field of an algebraic object that has a finite number of equivalence classes of indecomposable objects is to compute its Auslander algebra as the algebra of endomorphisms of a direct sum of all indecomposable representations (with one repres...

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Bibliographic Details
Date:2026
Main Authors: Bondarenko, V. M.; Інститут математики НАН України, Київ, Zubaruk, O. V.; Київський національний університет ім. Тараса Шевченка, Київ
Format: Article
Published: Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine 2026
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Online Access:http://journals.iapmm.lviv.ua/ojs/index.php/APMM/article/view/3653
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Journal Title:Prykladni Problemy Mekhaniky i Matematyky

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Prykladni Problemy Mekhaniky i Matematyky
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Summary:One way to describe the category of representations over a field of an algebraic object that has a finite number of equivalence classes of indecomposable objects is to compute its Auslander algebra as the algebra of endomorphisms of a direct sum of all indecomposable representations (with one representative from each class). The paper describes the Auslander algebra of the third order semigroup with the elements 0, b, c and the defining relations b2=0, c2=c, bc=0, cb=b, the unique, up to isomorphism, non-commutative semigroup of order three which contains a non-zero nilpotent element. The case of commutative third order semigroups were considered by the authors earlier.  Cite as: V. M. Bondarenko, M. V. Styopochkina, “Classification of the Auslander algebras of the unique non-commutative third order semigroup with a non-zero nilpotent element,” Прикл. проблеми механіки і математики, Issue 23, 5–10 (2025) (in Ukrainian), https://doi.org/10.15407/apmm2025.23.5-10
DOI:10.15407/3653