http://dspace.nbuv.gov.ua:80/handle/123456789/150337 Sat, 18 Apr 2026 14:16:54 GMT 2026-04-18T14:16:54Z http://dspace.nbuv.gov.ua:80/bitstream/id/448083/ http://dspace.nbuv.gov.ua:80/handle/123456789/150337 http://dspace.nbuv.gov.ua:80/handle/123456789/156627 Extended G-vertex colored partition algebras as centralizer algebras of symmetric groups Parvathi, M.; Kennedy, A.J. The Partition algebras Pk(x) have been defined in [M1] and [Jo]. We introduce a new class of algebras for every group G called “Extended G-Vertex Colored Partition Algebras," denoted by Pbk(x,G), which contain partition algebras Pk(x), as subalgebras. We generalized Jones result by showing that for a finite group G, the algebra Pbk(n,G) is the centralizer algebra of an action of the symmetric group Sn on tensor space W⊗k , where W = C n|G| . Further we show that these algebras Pbk(x,G) contain as subalgebras the “G-Vertex Colored Partition Algebras Pk(x,G)," introduced in [PK1]. Sat, 01 Jan 2005 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/156627 2005-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/156626 Some properties of primitive matrices over Bezout B-domain Shchedryk, V.P. The properties of primitive matrices (matrices for which the greatest common divisor of the minors of maximal order is equal to 1) over Bezout B - domain, i.e. commutative domain finitely generated principal ideal in which for all a,b,c with (a,b,c) = 1,c 6= 0, there exists element r ∈ R, such that (a+rb,c) = 1 is investigated. The results obtained enable to describe invariants transforming matrices, i.e. matrices which reduce the given matrix to its canonical diagonal form. Sat, 01 Jan 2005 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/156626 2005-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/156624 Steiner P-algebras Chakrabarti, S. General algebraic systems are able to formalize problems of different branches of mathematics from the algebraic point of view by establishing the connectivity between them. It has lots of applications in theoretical computer science, secure communications etc. Combinatorial designs play significant role in these areas. Steiner Triple Systems (STS) which are particular case of Balanced Incomplete Block Designs (BIBD) from combinatorics can be regarded as algebraic systems. Steiner quasigroups (Squags) and Steiner loops (Sloops) are two well known algebraic systems which are connected to STS. There is a one-to-one correspondence between STS and finite Squags and finite Sloops. A new algebraic system w.r.to a ternary operation P based on a Steiner Triple System introduced in [3]. In this paper the abstraction and the generalization of the properties of the ternary operation defined in [3] has been made. A new class of algebraic systems Steiner P-algebras has been introduced. The one-to-one correspondence between STS on a linearly ordered set and finite Steiner P-algebras has been established. Some identities have been proved. Sat, 01 Jan 2005 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/156624 2005-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/156622 A letter to ADM Editorial board Varbanets, P.D.; Savastru, O.V. Sat, 01 Jan 2005 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/156622 2005-01-01T00:00:00Z