Algebra and Discrete Mathematics. - № 1 (27). - 2019

On the Fitting ideals of a multiplication module

Tue, 01 Jan 2019 00:00:00 GMT

On the Fitting ideals of a multiplication module Hadjirezaei, S.; Karimzadeh, S. In this paper, we characterize all finitely gene- rated multiplication R-modules whose the first nonzero Fitting ideal of them is contained in only finitely many maximal ideals. Also, we prove that a finitely generated multiplication R-module M is faithful if and only if M is a projective of constant rank one R-module. Hadjirezaei S. On the Fitting ideals of a multiplication module / S. Hadjirezaei , S.Karimzadeh // Algebra and Discrete Mathematics. - 2019. - Vol. 27. - Number 1. - Рp. 27-34

Gram matrices and Stirling numbers of a class of diagram algebras

Tue, 01 Jan 2019 00:00:00 GMT

Gram matrices and Stirling numbers of a class of diagram algebras B i, N . K.; Parvathi, M . In this paper, we introduce Gram matrices for the signed partition algebras, the algebra of Z2-relations and the par- tition algebras. The nondegeneracy and symmetic nature of these Gram matrices are establised. Also, (s1, s2, r1, r2, p1, p2)-Stirling numbers of the second kind for the signed partition algebras, the algebra of Z2-relations are introduced and their identities are estab- lished. Stirling numbers of the second kind for the partition algebras are introduced and their identities are established. Bi N. K Gram matrices and Stirling numbers of a class of diagram algebras / N. K. la Bi, M. Parvathi // Algebra and Discrete Mathematics. - 2019. - Vol. 27. - Number 1. - Рp. 73-97

On free vector balleans

Tue, 01 Jan 2019 00:00:00 GMT

On free vector balleans Protasov, I.; Protasova, K. A vector balleans is a vector space over R en- dowed with a coarse structure in such a way that the vector opera- tions are coarse mappings. We prove that, for every ballean (X, E), there exists the unique free vector ballean V(X, E) and describe the coarse structure of V(X, E). It is shown that normality of V(X, E) is equivalent to metrizability of (X, E). Protasov I.On free vector balleans / I.Protasov , K.Protasova // Algebra and Discrete Mathematics. - 2019. - Vol. 27. - Number 1. - Рp.70-74

On hereditary reducibility of 2-monomial matrices over commutative rings

Tue, 01 Jan 2019 00:00:00 GMT

On hereditary reducibility of 2-monomial matrices over commutative rings Bondarenko, V. M.; Gildea, J.; Tylyshchak, A. A.; Yurchenko, N.V. A 2-monomial matrix over a commutative ring R is by definition any matrix of the form M(t, k, n) = Φ Ik 0 0 tIn−k , 0 < k < n, where t is a non-invertible element of R, Φ the companion matrix to λ n − 1 and Ik the identity k × k-matrix. In this paper we introduce the notion of hereditary reducibility (for these matrices) and indicate one general condition of the introduced reducibility. Bondarenko V. M. On hereditary reducibility of 2-monomial matrices over commutative rings / V. M. Bondarenko, J. Gildea, A. A. Tylyshchak, N.V.Yurchenko // Algebra and Discrete Mathematics. - 2019. - Vol. 27. - Number 1. - Рp.1 -11