http://hdl.handle.net/123456789/4382 2026-03-16T21:23:09Z http://hdl.handle.net/123456789/4522 Gram matrices and Stirling numbers of a class of diagram algebras Bi, N. K. In the paper [6], we introduced Gram matrices for the signed partition algebras, the algebra of Z2-relations and the partition algebras. (s1, s2, r1, r2, p1, p2)-Stirling numbers of the second kind are also introduced and their identities are established. In this paper, we prove that the Gram matrix is similar to a matrix which is a direct sum of block submatrices. As a consequence, the semisimplicity of a signed partition algebra is established. Bi N. K. Gram matrices and Stirling numbers of a class of diagram algebras / N. K. Bi, M. Parvathi // Algebra and Discrete Mathematics. - 2018. - Vol. 25. - Number 2. - Рp.215- 256 2018-01-01T00:00:00Z http://hdl.handle.net/123456789/4520 Some more algebra on ultrafilters in metric spaces Protasov, I . We continue algebraization of the set of ultrafilters on a metric spaces initiated in [6]. In particular, we define and study metric counterparts of prime, strongly prime and right cancellable ultrafilters from the Stone-Čech compactification of a discrete group as a right topological semigroup . Our approach is based on the concept of parallelity introduced in the context of balleans in. Protasov I. Some more algebra on ultrafilters in metric spaces / I . Protasov // Algebra and Discrete Mathematics. - 2018. - Vol. 25. - Number 2. - Рp. 286 - 293 2018-01-01T00:00:00Z http://hdl.handle.net/123456789/4516 On functional equations and distributive second order formulae with specialized quantifiers Movsisyan, Yu. The structure of invertible algebras with distributive second order formulae with specialized quantifiers is given. Asa consequence, the applications for solutions of the some functional equations of distributivity on quasigroups are provided. Movsisyan Yu . On functional equations and distributive second order formulae with specialized quantifiers / Yu . Movsisyan // Algebra and Discrete Mathematics. - 2018. - Vol. 25. - Number 2. - Рp. 269- 285 2018-01-01T00:00:00Z http://hdl.handle.net/123456789/4515 The growth function of the adding machine Skochko, V. We compute the growth function of the generalized adding machine and show that its generating function is not algebraic. V. Skochko The growth function of the adding machine / V. Skochko // Algebra and Discrete Mathematics. - 2018. - Vol. 25. - Number 2. - Рp. 303 - 310 2018-01-01T00:00:00Z