For any two positive integers m, n, we denote the graph Km,n ⊙ K₁ by G. Ma Ke-Jie proposed a conjecture [9] that pendant edge extension of a complete bipartite graph is a k-graceful graph for k > 2. In this paper we prove ...

Lie algebras are exactly the anticommutative Leibniz algebras. In this article, we conduct a brief analysis of the approach to Leibniz algebras which based on the concept of the anti-center (Lie-center) and antinilpotency ...

Let R ⊆ S be a ring extension, and let A be an R-submodule of S. The saturation of A (in S) by τ is set A[τ] = {x ∈ S : tx ∈ A for some t ∈ τ}, where τ is a multiplicative subset of R. We study properties of saturations ...

An analogue of the Wedderburn Principal Theorem (WPT) is considered for finite-dimensional Jordan superal-gebras A with solvable radical N, N² = 0, and such that A/N ≅ Jospn|2m(F), where F is a field of characteristic zero. ...

The rings considered in this article are nonzero commutative with identity which are not fields. Let R be a ring. We denote the collection of all proper ideals of R by I(R) and the collection I(R)\{(0)} by I(R)*. Recall ...

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 ...

The paper deals with methods of constructing square difference labeling of caterpillars and graphs derived from two operations: path union of cycles and disjoint union of stars. The existence of the square difference ...

This article deals mostly with the following question: when the classical ring of quotients of a commutative ring is a ring of stable range 1? We introduce the concepts of a ring of (von Neumann) regular range 1, a ring ...

In this paper we consider the ordered by inclusion lattice Part(M) of all partitions of a countable set M. The lattice Part(M) is a semigroup with respect to the operation Λ which maps two partitions to their greatest ...

We give a classification of representations of the Kleinian 4-group up to weak equivalence.