http://dspace.nbuv.gov.ua:80/handle/123456789/150369 Wed, 22 Apr 2026 10:44:39 GMT 2026-04-22T10:44:39Z http://dspace.nbuv.gov.ua:80/bitstream/id/448115/ http://dspace.nbuv.gov.ua:80/handle/123456789/150369 http://dspace.nbuv.gov.ua:80/handle/123456789/154856 Diagonalizability theorem for matrices over certain domains Zabavsky, B.; Domsha, O. It is proved that R is a commutative adequate domain, then R is the domain of stable range 1 in localization in multiplicative closed set which corresponds s-torsion in the sense of Komarnitskii. Sat, 01 Jan 2011 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/154856 2011-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154821 H -supplemented modules with respect to a preradical Yahya Talebi; A. R. Moniri Hamzekolaei; Derya Keskin Tutuncu Let M be a right R-module and τ a preradical. We call M τ-H-supplemented if for every submodule A of M there exists a direct summand D of M such that (A+D)/D⊆τ(M/D) and (A+D)/A⊆τ(M/A). Let τ be a cohereditary preradical. Firstly, for a duo module M=M₁⊕M₂ we prove that M is τ-H-supplemented if and only if M₁ and M₂ are τ-H-supplemented. Secondly, let M=⊕ⁿi=1Mi be a τ-supplemented module. Assume that Mi is τ-Mj-projective for all j>i. If each Mi is τ-H-supplemented, then M is τ-H-supplemented. We also investigate the relations between τ-H-supplemented modules and τ-(⊕-)supplemented modules. Sat, 01 Jan 2011 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/154821 2011-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154775 Graded limits of minimal affinizations and beyond: the multiplicity free case for type E₆ Moura, A.; Pereira, F. e obtain a graded character formula for certain graded modules for the current algebra over a simple Lie algebra of type E₆. For certain values of their highest weight, these modules were conjectured to be isomorphic to the classical limit of the corresponding minimal affinizations of the associated quantum group. We prove that this is the case under further restrictions on the highest weight. Under another set of conditions on the highest weight, Chari and Greenstein have recently proved that they are projective objects of a full subcategory of the category of graded modules for the current algebra. Our formula applies to all of these projective modules. Sat, 01 Jan 2011 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/154775 2011-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154770 Characterization of finite simple semigroup digraphs Meksawang, J.; Panma, S.; Knauer, U. This paper characterizes directed graphs which are Cayley graphs of finite simple semigroups, i.e. of a subspecies of completely regular semigroups. Moreover we investigate the structure of Cayley graphs of finite simple semigroups with a one-element connection set. We introduce the conditions for which they are isomorphic and connected. Sat, 01 Jan 2011 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/154770 2011-01-01T00:00:00Z