Algebra and Discrete Mathematicshttp://dspace.nbuv.gov.ua:80/handle/123456789/566282024-10-10T20:25:27Z2024-10-10T20:25:27ZOn certain semigroups of contraction mappings of a finite chainUmar, A.Zubairu, M.M.http://dspace.nbuv.gov.ua:80/handle/123456789/1887552023-03-14T23:27:29Z2021-01-01T00:00:00ZOn certain semigroups of contraction mappings of a finite chain
Umar, A.; Zubairu, M.M.
Let [n] = {1, 2, . . . , n} be a finite chain and let Pn (resp. , Tn) be the semigroup of partial transformations on [n] (resp. , full transformations on [n]). Let CPn = {α ∈ Pn : (for all x, y ∈ Dom α) |xα−yα| ≤ |x−y|} (resp. , CT n = {α ∈ Tn : (for all x, y ∈ [n]) |xα−yα| ≤ |x−y|} ) be the subsemigroup of partial contraction mappings on [n] (resp. , subsemigroup of full contraction mappings on [n]). We characterize all the starred Green’s relations on CPn and it subsemigroup of order preserving and/or order reversing and subsemigroup of order preserving partial contractions on [n], respectively. We show that the semigroups CPn and CT n, and some of their subsemigroups are left abundant semigroups for all n but not right abundant for n ≥ 4. We further show that the set of regular elements of the semigroup CT n and its subsemigroup of order preserving or order reversing full contractions on [n], each forms a regular subsemigroup and an orthodox semigroup, respectively.
2021-01-01T00:00:00ZSome commutativity criteria for 3-prime near-ringsRaji, A.http://dspace.nbuv.gov.ua:80/handle/123456789/1887542023-03-14T23:27:27Z2021-01-01T00:00:00ZSome commutativity criteria for 3-prime near-rings
Raji, A.
In the present paper, we introduce the notion of *-generalized derivation in near-ring N and investigate some properties involving that of *-generalized derivation of a *-prime near-ring N which forces N to be a commutative ring. Some properties of generalized semiderivations have also been given in the context of 3-prime near-rings. Consequently, some well known results have been generalized. Furthermore, we will give examples to demonstrate that the restrictions imposed on the hypothesis of various results are not superŕuous.
2021-01-01T00:00:00ZA study on dual square free modulesMedina-Bárcenas, M.Keskin Tütüncü, D.Kuratomi, Y.http://dspace.nbuv.gov.ua:80/handle/123456789/1887532023-03-14T23:27:28Z2021-01-01T00:00:00ZA study on dual square free modules
Medina-Bárcenas, M.; Keskin Tütüncü, D.; Kuratomi, Y.
Let M be an H-supplemented coatomic module with FIEP. Then we prove that M is dual square free if and only if every maximal submodule ofM is fully invariant. Let M = ⊕ i∈I Mi be a direct sum, such that M is coatomic. Then we prove that M is dual square free if and only if each Mi is dual square free for all i ∈ I and, Mi and ⊕ j̸≠i Mj are dual orthogonal. Finally we study the endomorphism rings of dual square free modules. Let M be a quasi-projective module. If EndR(M) is right dual square free, then M is dual square free. In addition, if M is finitely generated, then EndR(M) is right dual square free whenever M is dual square free. We give several examples illustrating our hypotheses.
2021-01-01T00:00:00ZHomotopy equivalence of normalized and unnormalized complexes, revisitedLyubashenko, V.Matsui, A.http://dspace.nbuv.gov.ua:80/handle/123456789/1887522023-03-14T23:27:23Z2021-01-01T00:00:00ZHomotopy equivalence of normalized and unnormalized complexes, revisited
Lyubashenko, V.; Matsui, A.
We consider the unnormalized and normalized complexes of a simplicial or a cosimplicial object coming from the DoldśKan correspondence for an idempotent complete additive category (kernels and cokernels are not required). The normalized complex is defined as the image of certain idempotent in the unnormalized complex. We prove that this idempotent is homotopic to identity via homotopy which is expressed via faces and degeneracies. Hence, the normalized and unnormalized complex are homotopy isomorphic to each other. We provide explicit formulae for the homotopy.
2021-01-01T00:00:00Z