Asian-European Journal of Mathematics

Let R be a ring, (S, ≤) a strictly ordered monoid and ω : S → End(R) a monoid homomorphism. In this paper, we study the triangular matrix representation of skew generalized power series ring R[[S, ω]] which is a compact generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomials rings, (skew) Laurent power series rings, (skew) group rings, (skew) monoid rings, Mal'cev–Neumann rings and generalized power series rings. We investigate that if R is S-compatible and (S, ω)-Armendariz, then the skew generalized power series ring has same triangulating dimension as R. Furthermore, if R is a PWP ring, then skew generalized power series is also PWP ring.

A subset M of a given basic algebra is MP-closed if a ∈ M and a → b ∈ M always imply b ∈ M for b ≤ a. We get a characterization of MP-closed subsets for commutative basic algebras in terms of closedness in the derived operation ⊙. If, moreover, the basic algebra is a chain, then a particular simple condition is derived. For basic algebras which are not commutative we derive only a closedness with respect to the deduction rule Modus Tollens.

It is known that there is a Galois connection between submonoids of the monoid consisting of all hypersubstitutions and complete sublattices of the lattice of all varieties of the same type. It is of interest to know which semigroup properties of hypersubstitutions can be transferred by this Galois connection. In this paper, we characterize regular weak projection hypersubstitutions of all mappings from the set of operation symbols to the set of terms which preserve arities type (2,2).

In this paper, we prove common fixed point theorems for weakly compatible mappings in Non-Archimedean Menger PM-spaces employing common property (E.A). Some examples are derived which demonstrate the validity of our results. As an application to our main result, we present a fixed point theorem for four finite families of self mappings. Our results improve and extend several existing results in the literature.

In this paper, several theorems of Macdonald [On certain varieties of groups, Math. Z.76 (1961) 270–282; On certain varieties of groups II, Math. Z.78 (1962) 175–188] on the varieties of nilpotent groups will be generalized to the case of Lie rings. We consider three varieties of Lie rings of any characteristic associated with some equations (see Eqs. (1.1)–(1.3)). We prove that each Lie ring in variety (1.1) is nilpotent of exponent at most n + 2; if L is a Lie ring in variety (1.2), then L² is nilpotent of exponent at most n + 1; and each Lie ring in variety (1.3) is solvable of length at most n + 1. We also discuss some varieties of solvable Lie rings and the varieties of Lie rings defined by the properties of subrings.

In this work, we study some properties of a certain class of meromorphic functions defined by means of the Hadamard product of Cho–Kwon–Srivastava operator. We also define here a similar transformation by means of an operator given by Ghanim and Darus and study its properties.

Let >M and N be two R-modules. N_R is called singular M-p-injective if for every singular M-cyclic submodule X of M_R, every homomorphism from X to N can be extended to a homomorphism from M to N. M_R is quasi-singular prinicipally injective if M is a singular M-p-injective module. It is shown that a ring R is right non-singular if and only if every right R-module is singular R-p-injective if and only if factors of singular R-p-injective modules are singular R-p-injective. A singular R-module M is injective if and only if M is N-sp-injective for every R-module N. Finally, we characterize quasi-sp-injective modules in terms of their endomorphism rings.

This paper is concerned with the optimality for generalized semi-infinite programming (GSIP) with nondifferentiable and nonconvex (but being regular in Clarke sense) constraint functions. The objective function is only locally Lipschitz. We consider a lower level constraint qualification which is based on the Clarke subdifferential. This constraint qualification is a natural extension of Mangasarian–Fromovitz one to the differentiable GSIP. The main results are Fritz-John type necessary conditions for optimal solutions.

In this paper we have developed a graphical technique by which a suitably created fragment of a coset diagram for the action of PSL(2, ℤ) on projective lines over Galois fields can be used to obtain a complete coset diagram depicting finite homomorphic images of groups Δ(2, 3, k) = 〈x, y : x² = y³ = (xy)^k = 1〉.

In this paper we obtain means which involve divided differences for n-convex functions. We examine their monotonicity property using exponentially convex functions.

The concept of σ-ideals is introduced in almost distributive lattices (ADLs). Generalized stone ADLs are characterized in terms of their σ-ideals and α-ideals. Normal ADLs are also characterized in terms of their O-ideals and σ-ideals. Finally, a discussion is made about the epimorphic images and inverse images of σ-ideals.

In this paper we show that: if G is a totally ordered group and R is a G-Armendariz ring (an NI ring with nil(R) is nilpotent), then the ring Λ = R((G; σ; τ)) of Mal'cev–Neumann series is a right zip (weak zip) ring if and only if R is.

Let (L, N) be a pair of finite-dimensional nilpotent Lie algebras, in which N is an ideal in L. In this paper we derive some inequalities for the dimension of the Schur multiplier of the pair (L, N) in terms of the dimension of the commutator subalgebra [L, N].

For defining a K-semialgebra A, we use Katsov's tensor product which makes the category K-Smod monoidal. Further, if A is a K-semialgebra then A^Δ is a K^Δ-algebra and A embeds in A^Δ. The subtractive and strong partial actions of a group are defined on A. A subtractive partial action α of a group G on A can be extended to a partial action of G on A^Δ which helps in globalization of α. A strong partial action on A has a unique subtractive globalization. We also discuss the associativity of the skew group semiring A ×_α G.

We obtained some sufficient and necessary conditions of existence of faithful irreducible representations of a soluble group G of finite rank over a field k. It was shown that the existence of such representations strongly depends on construction of the socle of the group G. The situation is especially complicated in the case where the field k is locally finite.