In this paper we are concerned with the following question: for a semigroup S, what is the largest size of a subsemigroup T ≤ S where T has a given property? The semigroups S that we consider are the full transformation semigroups; all mappings from a finite set to itself under composition of mappings. The subsemigroups T that we consider are of one of the following types: left zero, right zero...

We consider three operators which appear naturally in convexity theory and determine completely the structure of the semigroup generated by them.

We completely determine all distributive, codistributive, standard, costandard, and neutral elements in the lattice of overcommutative semigroup varieties, thus correcting a gap contained in [5].

This paper examines actions of right LCM semigroups by endomorphisms C*-algebras that encode an additional structure the semigroup. We define contractive covariant representations for these semigroup dynamical systems and prove a generalized Stinespring's dilation theorem showing can be dilated if only map on C*-algebra is unital completely positive. generalizes earlier results about dilations ...

The intuitionistic fuzzification of the notion of a bi-ideal in ordered semigroups is considered. In terms of intuitionistic fuzzy set, conditions for an ordered semigroup to be completely regular is provided. Characterizations of intuitionistic fuzzy bi-ideals in ordered semigroups are given. Using a collection of bi-ideals with additional conditions, an intuitionistic fuzzy bi-ideal is constr...

We consider a very simple Mealy machine (two non-trivial states over a two-symbol alphabet), and derive some properties of the semigroup it generates. It is an infinite, finitely generated semigroup, and we show that the growth function of its balls behaves asymptotically like nα, for α = 1 + log 2/log 1+ √ 5 2 ; that the semigroup satisfies the identity g = g; and that its lattice of two-sided...

We consider a very simple Mealy machine (three states over a twosymbol alphabet), and derive some properties of the semigroup it generates. In particular, this is an infinite, finitely generated semigroup; we show that the growth function of its balls behaves asymptotically like nα, for α = 1 + log 2/log 1+ √ 5 2 ; that the semigroup satisfies the identity g = g; and that its lattice of two-sid...

We develop a general approach to the study of maximal nilpotent subsemigroups of finite semigroups. This approach can be used to recover many known classifications of maximal nilpotent subsemigroups, in particular, for the symmetric inverse semigroup, the symmetric semigroup, and the factor power of the symmetric group. We also apply this approach to obtain a classification of maximal nilpotent...

A class of differential Riccati equations (DREs) is considered whereby the evolution of any solution can be identified with the propagation of a value function of a corresponding optimal control problem arising in L2-gain analysis. By exploiting the semigroup properties inherited from the attendant dynamic programming principle, a max-plus primal space fundamental solution semigroup of max-plus...