In this paper we present a Galois-Grothendiecktype correspondence for groupoid actions. As an application a Galois-type correspondence is also given.

Given a subset D of positive integers, an integer distance graph is a graph G(Z, D) with the set Z of integers as vertex set and with an edge joining two vertices u and v if and only if |u−v| ∈ D. In this paper we consider ...

We study connections between wildness of the problem of classifying the matrices over an integral domain up to equivalence modulo an ideal and properties of the set of prime elements of the domain.

Let R be a ring with an endomorphism σ. We introduce (σ, 0)-multiplication which is a generalization of the simple 0- multiplication. It is proved that for arbitrary positive integers m ≤ n and n ≥ 2, R[x; σ] is a reduced ...

Let Xn = {1,2,…,n}. On a partial transformation α : Dom α ⊆ Xn → Im α ⊆ Xn of Xn the following parameters are defined: the breadth or width of α is ∣ Dom α ∣, the collapse of α is c(α) = ∣ ∪t∈Imα{tα⁻¹ :∣ tα⁻¹ ∣≥ 2} ∣, fix ...