A ?semigroup is a semigroup whose lattice of congruences is a chain with respect to inclusion. Schein 9] and Tamura 11] have investigated commutative ?semigroups, Trotter 13] exponential, Nagy 4] weakly exponential and Bonzini and Cherubini Spoletini 2] nite ?semigroups. The pupose of the present paper is to investigate archimedean weakly commutative and H?commutative ?semigroups. 1 Weakly comm...

We study C*-algebras associated with subsemigroups of groups. For a large class of such semigroups including positive cones in quasi-lattice ordered groups and left Ore semigroups, we describe the corresponding semigroup C*algebras as C*-algebras of inverse semigroups, groupoid C*-algebras and full corners in associated group crossed products. These descriptions allow us to characterize nuclear...

Last years a number of papers were devoted to describing automorphisms of semigroups of endomorphisms of free finitely generated universal algebras of some varieties: groups, semigroups, associative commutative algebras, inverse semigroups, modules, Lie algebras and some others (see references). All these researches were inspired by the questions prof. B. Plotkin set in connection with so calle...

It is studied how taking the inverse image by a sliding block code affects the syntactic semigroup of a sofic subshift. Two independent approaches are used: ζ-semigroups as recognition structures for sofic subshifts, and relatively free profinite semigroups. A new algebraic invariant is obtained for weak equivalence of sofic subshifts, by determining which classes of sofic subshifts naturally d...