In [1,2,3], A. C. Baker and J.W. Baker studied the subspace Ma(S) of the convolution measure algebra M, (S) of a locally compact semigroup. H. Dzinotyiweyi in [5,7] considers an analogous measure space on a large class of C-distinguished topological semigroups containing all completely regular topological semigroups. In this paper, we extend the definitions to study the weighted semigroup ...

Semigroups whose congruences form a chain are often termed ∆-semigroups. The commutative ∆-semigroups were determined by Schein and by Tamura. A natural generalization of commutativity is permutativity: a semigroup is permutative if it satisfies a non-identity permutational identity. We completely determine the permutative ∆-semigroups. It turns out that there are only six noncommutative exampl...

In this paper, we first introduce the new concept of completely semiprime fuzzy ideals of an ordered semigroup S, which is an extension of completely semiprime ideals of ordered semigroup S, and investigate some its related properties. Especially, we characterize an ordered semigroup that is a semilattice of simple ordered semigroups in terms of completely semiprime fuzzy ideals of ordered semi...

We introduce the notion of Gröbner S-basis of an ideal of the free associative algebra K〈X〉 over a field K invariant under the action of a semigroup S of endomorphisms of the algebra. We calculate the Gröbner S-bases of the ideal corresponding to the universal enveloping algebra of the free nilpotent of class 2 Lie algebra and of the T-ideal generated by the polynomial identity [x, y, z] = 0, w...

We consider properties of second-order operatorsH = − ∑d i,j=1 ∂i cij ∂j on R with bounded real symmetric measurable coefficients. We assume that C = (cij) ≥ 0 almost everywhere, but allow for the possibility that C is singular. We associate with H a canonical self-adjoint viscosity operator H0 and examine properties of the viscosity semigroup S generated by H0. The semigroup extends to a posit...

Consider a semigroup action on a set. We derive conditions, in terms of the induced action of the semigroup on {0, 1}-valued probability charges, which ensure that all invariant probability charges are strongly continuous.

This paper determines all pseudovarieties of nite semigroups whose powers are contained in DA. As an application, it is shown that it is computable, for a decidable pseudovariety V of aperiodic semigroups, the least exponent n such that the iterated power P n V is the pseudovariety of all nite semigroups.

A ternary semigroup is a nonempty set together with a ternary multiplication which is associative. Any semigroup can be reduced to a ternary semigroup but a ternary semigroup does not necessarily reduce to a semigroup. The notion of fuzzy sets was introduced by Zadeh in 1965 and that of rough sets by Pawlak in 1982. Applications of the fuzzy set theory and rough set theory have been found in va...

A new max-plus fundamental solution semigroup is presented for a class of lossless wave equations. This new semigroup is developed by employing the action principle to encapsulate the propagation of all possible solutions of a given wave equation in the evolution of the value function of an associated optimal control problem. The max-plus fundamental solution semigroup for this optimal control ...

The syntactic complexity of a regular language is the size of its syntactic semigroup. This semigroup is isomorphic to the transition semigroup of the minimal deterministic finite automaton accepting the language, that is, to the semigroup generated by transformations induced by non-empty words on the set of states of the automaton. In this paper we search for the largest syntactic semigroup of...