Graded near-rings

In this paper, we consider graded near-rings over a monoid G as generalizations of graded rings over groups, and study some of their basic properties. We give some examples of graded near-rings having various interesting properties, and we define and study the Gop-graded ring associated to a G-graded abelian near-ring, where G is a left cancellative monoid and Gop is its opposite monoid. We also compute the graded ring associated to the graded near-ring of polynomials (over a commutative ring R) whose constant term is zero.

IF-AUTOMORPHISMS OF A FREE SOLVABLE Sp-PERMUTABLE ALGEBRA OF A FINITE RANK OVER A LEFT CANCELLATIVE MONOID ARE PSEUDO-TAME

Consider a variety V of acts over a left cancellative monoid S that have a ternary Maltsev operation p(〈p, S〉- algebras ). Using the Magnus–Artamonov representation, the construction of the free Abelian extension of an arbitrary V-algebra was obtained and explored by the author. In the present article we prove that each IF-automorphism of a free k-step solvable V-algebra of a finite rank (k > 1) is pseudo-tame, i.e. it is presented as a product of elementary automorphisms of a special module over a ring with several objects.

REES MATRIX THEOREM FOR $\mathcal{D}^{(\ell)}$-SIMPLE STRONGLY RPP SEMIGROUPS

A semigroup S is called rpp if all right principal ideals of S, regarded as S1-systems, are projective. An rpp semigroup S is said to be strongly rpp if for any a ∈ S, there exists a unique idempotent e such that [Formula: see text] and a = ea. In this paper, we show that a [Formula: see text]-simple strongly rpp semigroup can be expressed by a Rees matrix semigroup over a left cancellative monoid and conversely. Our result generalizes the classical theorem of Rees in 1940 and also amplifies the Rees theorem in semigroup given by Lallement and Petrich in 1969.