Free k-nilpotent n-tuple semigroups

Abstract

An n-tuple semigroup is an algebra defined on a set with n binary associative operations. This notion play a prominent role in the theory of n-tuple algebras of associative type. Our paper is devoted to the development of the variety theory of n-tuple semigroups. We construct a free k-nilpotent n-tuple semigroup and characterize the least k-nilpotent congruence on a free n-tuple semigroup.

Keywords:

• Congruence
• free k-nilpotent n-tuple semigroup
• k-nilpotent n-tuple semigroup
• n-tuple semigroup
• semigroup

2020 Mathematics Subject Classification:

• 08B20
• 20M10
• 20M50
• 17A30
• 17D99

Acknowledgments

The authors are grateful to the referee for helpful suggestions.

Additional information

Funding

The authors were supported by Special Research Fellowships of the Erwin Schrödinger International Institute for Mathematics and Physics at the University of Vienna.