Equicontinuous commutative semigroups of onto functions

Varieties of Commutative Semigroups

In this paper, we describe all equational theories of commutative semigroups in terms of certain well-quasi-orderings on the set of finite sequences of nonnegative integers. This description yields many old and new results on varieties of commutative semigroups. In particular, we obtain also a description of the lattice of varieties of commutative semigroups, and we give an explicit uniform sol...

Totally Ordered Commutative Semigroups

Let 5( + , < ) be a system consisting of a set S endowed with an associative binary operation + and a total ( = linear = simple) order relation < . The composition + and the relation < may be connected by either or both of the following conditions. MC (Monotone Condition). If a and b are elements of 5 such that ax+y ...

Generation of Equicontinuous Semigroups by Hermitian and Sectorial Operators. I

Median and Center of Zero-Divisor Graph of Commutative Semigroups

For a commutative semigroup S with 0, the zero-divisor graph of S denoted by &Gamma(S) is the graph whose vertices are nonzero zero-divisor of S, and two vertices x, y are adjacent in case xy = 0 in S. In this paper we study median and center of this graph. Also we show that if Ass(S) has more than two elements, then the girth of &Gamma(S) is three.

Equations on Semidirect Products of Commutative Semigroups

In this paper; we study equations on semidirect products of commutative semigroups. Let Comq,r denote the pseudovariety of all finite semigroups that satisfy the equations xy = yx and x r + q = xr. The pseudovariety Com1,1 is the pseudovariety of all finite semilattices. We consider the product pseudovariety Comq,r * generated by all semidirect products of the form S*T with S ∈ Comq,r and T ∈ ,...