http://hdl.handle.net/123456789/4381 Wed, 15 Apr 2026 21:27:23 GMT 2026-04-15T21:27:23Z http://hdl.handle.net/123456789/4493 Closure operators in modules and adjoint functors Kashu, A. I. In the present work the relations between the closure operators of two module categories are investigated in the case when the given categories are connected by two covariant adjoint functors H : R-Mod −→ S-Mod and T : S-Mod −→ R-Mod. Two mappings are defined which ensure the transition between the closure operators of categories R-Mod and S-Mod. Some important properties of these mappings are proved. It is shown that the studied mappings are compatible with the order relations and with the main operations. Kashu A. I.Closure operators in modules and adjoint functors / A. I. Kashu // Algebra and Discrete Mathematics. - 2018. - Vol. 25. - Number 1. - Рp. 98-117 Mon, 01 Jan 2018 00:00:00 GMT http://hdl.handle.net/123456789/4493 2018-01-01T00:00:00Z http://hdl.handle.net/123456789/4492 Weak equivalence of representations of Kleinian 4-group Plakosh, A. We give a classification of representations of the Kleinian 4-group up to weak equivalence. Plakosh A. Weak equivalence of representations of Kleinian 4-group / A . Plakosh // Algebra and Discrete Mathematics. - 2018. - Vol. 25. - Number 1. - Рp.130-136 Mon, 01 Jan 2018 00:00:00 GMT http://hdl.handle.net/123456789/4492 2018-01-01T00:00:00Z http://hdl.handle.net/123456789/4485 Construction of a complementary quasiorder Jakubíková -Studenovská, D.; Janičková, L. For a monounary algebra A = (A, f) we study the lattice Quord A of all quasiorders of A, i.e., of all reflexive and transitive relations compatible with f. Monounary algebras (A, f) whose lattices of quasiorders are complemented were characterized in 2011 as follows: (∗) f(x) is a cyclic element for all x ∈ A, and all cycles have the same square-free number n of elements. Sufficiency of the condition (∗) was proved by means of transfinite induction. Now we will describe a construction of a complement to a given quasiorder of (A, f) satisfying (∗). Jakubíková -Studenovská D. Construction of a complementary quasiorder / D. Jakubíková -Studenovská , L. Janičková // Algebra and Discrete Mathematics. - 2019. - Vol. 27. - Number 1. - Рp. 39 -55 Mon, 01 Jan 2018 00:00:00 GMT http://hdl.handle.net/123456789/4485 2018-01-01T00:00:00Z http://hdl.handle.net/123456789/4481 A way of computing the Hilbert series Haider, A. Let S = K[x1, x2, . . . , xn] be a standard graded K-algebra for any field K. Without using any heavy tools of com- mutative algebra we compute the Hilbert series of graded S-module S/I, where I is a monomial ideal. Haider A. A way of computing the Hilbert series / A. Haider // Algebra and Discrete Mathematics. - 2019. - Vol. 27. - Number 1. - Рp. 35 -38 Mon, 01 Jan 2018 00:00:00 GMT http://hdl.handle.net/123456789/4481 2018-01-01T00:00:00Z