Algebra and Discrete Mathematics. - № 1 (27). - 2019
http://hdl.handle.net/123456789/4380
This is a special issue of our journal devoted to the 75th anniversary of the birth of Volodymyr Kyrychenko2022-09-17T06:00:59ZOn the Fitting ideals of a multiplication module
http://hdl.handle.net/123456789/4419
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
2019-01-01T00:00:00ZGram matrices and Stirling numbers of a class of diagram algebras
http://hdl.handle.net/123456789/4418
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
2019-01-01T00:00:00ZOn free vector balleans
http://hdl.handle.net/123456789/4417
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
2019-01-01T00:00:00ZOn hereditary reducibility of 2-monomial matrices over commutative rings
http://hdl.handle.net/123456789/4416
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
2019-01-01T00:00:00Z