Algebra and Logic Seminar

The next meeting of the seminar will be held on November 17, 2017 (Friday), at 13:00, in Room 578 of the Institute of Mathematics and Informatics.

A talk on

n-TUPLE SEMIGROUPS

will be delivered by Anatolii V. ZHUCHOK, Luhansk Taras Shevchenko National University, Starobilsk, Ukraine.

Everybody is invited.

Abstract. An n-tuple semigroup is an algebraic system consisting of a set with n binary associative operations satisfying certain equations. n-Tuple semigroups play a prominent role in the theory of non-associative rings and algebras. They are a generalization of semigroups and have relationships with such algebraic structures as interassociative semigroups, restrictive bisemigroups, doppelsemigroups and trioids.

Examples of n-tuple semigroups are given and the independence of axioms of an n-tuple semigroup is established. Elements of the variety theory of n-tuple semigroups are outlined. n-Tuple semigroups which are free in the variety of n-tuple semigroups are constructed and the least congruences on free n-tuple semigroups are investigated. The free product of n-tuple semigroups is presented and its structure is described. Automorphism groups of constructed free algebras are characterized.