Digital Repository of Luhansk Taras Shevchenko National University

# Browsing Algebra and Discrete Mathematics. - № 1 (23). - 2017 by Title

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• (ДЗ "ЛНУ імені Тараса Шевченка", 2017)
In this paper we introduce the notion of the neat range one for Bezout duo-domains. We show that a distributive Bezout domain is an elementary divisor domain if and only if it is a duo-domain of neat range one.
• (ДЗ "ЛНУ імені Тараса Шевченка", 2017)
We present a simplified way to construct the Gelfand-Tsetlin modules over gl(n, C) related to a 1-singular GT- tableau defined in . We begin by reframing the classical construc- tion of generic Gelfand-Tsetlin ...
• (ДЗ "ЛНУ імені Тараса Шевченка", 2017)
We develop the theory dg algebras with enough idempotents and their dg modules and show their equivalence with that of small dg categories and their dg modules. We introduce the concept of dg adjunction and show that ...
• (ДЗ "ЛНУ імені Тараса Шевченка", 2017)
We introduce the equivalence relation ρ on the set of Carter diagrams and construct an explicit transformation of any Carter diagram containing l-cycles with l > 4 to an equivalent Carter diagram containing only 4-cycles. ...
• (ДЗ "ЛНУ імені Тараса Шевченка", 2017)
In this survey we discuss the theory of Galois rings and orders developed in by Sergey Ovsienko and the first author. This concept allows to unify the representation theories of Generalized Weyl Algebras and of the ...
• (ДЗ "ЛНУ імені Тараса Шевченка", 2017)
We study representations of the group of order 2 over local factorial rings of characteristic not 2 with residue field of characteristic 2. The main results are related to a sufficient condition of wildness of groups.
• (ДЗ "ЛНУ імені Тараса Шевченка", 2017)
A finite dimensional Jordan algebra J over a field k is called basic if the quotient algebra J/ Rad J is isomorphic to a direct sum of copies of k. We describe all basic Jordan algebras J with (Rad J) 2 = 0 of finite and ...
• (2017)
We define representation types of nodal algebras of type E.