We construct a simplified resolution for the trivial G-module Z, where G is a finite abelian group, and compare it with the standard resolution. We use it to calculate cohomologies of irreducible G-lattices and their duals.

The notions of (G,ϕ)-crossed product and quasicrossed system are introduced in the setting of (G,ϕ)-quasiassociative algebras, i.e., algebras endowed with a grading by a group G, satisfying a ``quasiassociative'' law. It ...

In this paper we study the properties of positive series such that its terms are reciprocals of the elements of Jacobsthal-Lucas sequence. In particular, we consider the properties of the set of incomplete sums as well as ...

Let K be an algebraically closed field of characteristic zero and A a field of algebraic functions in n variables over K. (i.e. A is a finite dimensional algebraic extension of the field K(x1,…,xn) ). If D is a K-derivation ...

We introduce quantum Boolean algebras which are the analogue of the Weyl algebras for Boolean affine spaces. We study quantum Boolean algebras from the logical and the set theoretical viewpoints.

Let D=(V,A) be a finite simple directed graph (shortly digraph). A function f:V⟶{−1,1} is called a twin signed dominating function (TSDF) if f(N⁻[v])≥1 and f(N⁺[v])≥1 for each vertex v∈V. The twin signed domination number ...