7 citations · 8 across the 7 of their papers we have counts for
9 papers
On congruence-semisimple semirings and the -group characterization of ultramatricial algebras over semifields
Yefim Katsov, Tran Giang Nam, Jens Zumbrägel
In this paper, we provide a complete description of congruence-semisimple semirings and introduce the pre-ordered abelian Grothendieck groups and of the isomorph…
Toward Homological Characterization of Semirings by e-Injective Semimodules
J. Y. Abuhlail, S. N. Il'in, Y. Katsov +1
In this paper, we introduce and study e-injective semimodules, in particular over additively idempotent semirings. We completely characterize semirings all of whose semimodules are…
Toward Homological Structure Theory of Semimodules: On Semirings All of Whose Cyclic Semimodules Are Projective
S. N. Il'in, Y. Katsov, T. G. Nam
In this paper, we introduce homological structure theory of semirings and CP-semirings---semirings all of whose cyclic semimodules are projective. We completely describe semisimple…
On V-Semirings and Semirings all of whose Cyclic Semimodules are Injective
J. Y. Abuhlail, S. N. Il'in, Y. Katsov +1
In this paper, we introduce and study V- and CI-semirings---semirings all of whose simple and cyclic, respectively, semimodules are injective. We describe V-semirings for some clas…
On Radicals of Semirings and Related Problems
Y. Katsov, T. G. Nam
The aim of this paper is to develop an `external' Kurosh-Amitsur radical theory of semirings and, using this approach, to obtain some fundamental results regarding two Jacobson typ…
On geometrically equivalent S-acts
Yefim Katsov
In this paper, considering the geometric equivalence for algebras of a variety of S-acts over a monoid S, we obtain representation theorems describing all types of the equi…