Structure of relatively free n-tuple semigroups-Reference-Cited by-同舟云学术

Structure of relatively free n-tuple semigroups

Published:2023 Issue:1 Volume:36 Page:109-128
ISSN:1726-3255
Container-title:Algebra and Discrete Mathematics
language:
Short-container-title:ADM

Author:

Zhuchok Anatolii,

Abstract

An n-tuple semigroup is an algebra defined on a set with n binary associative operations. This notion was considered by Koreshkov in the context of the theory of n-tuple algebras of associative type. The n>1 pairwise interassociative semigroups give rise to an n-tuple semigroup. This paper is a survey of recent developments in the study of free objects in the variety of n-tuple semigroups. We present the constructions of the free n-tuple semigroup, the free commutative n-tuple semigroup, the free rectangular n-tuple semigroup, the free left (right) k-nilpotent n-tuple semigroup, the free k-nilpotent n-tuple semigroup, and the free weakly k-nilpotent n-tuple semigroup. Some of these results can be applied to constructing relatively free cubical trialgebras and doppelalgebras.

Publisher

Luhansk Taras Shevchenko National University

Subject

Discrete Mathematics and Combinatorics,Algebra and Number Theory

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