Free left n-trinilpotent trioids

Abstract

Loday and Ronco introduced the notion of a trioid and presented the free trioid of rank 1. We introduce the variety of left (right) n-trinilpotent trioids which are analogs of left (right) nilpotent semigroups of rank n considered by Schein, and construct the free left (right) n-trinilpotent trioid.

Keywords:

• Free left n-trinilpotent trioid
• left n-trinilpotent trioid
• semigroup
• trioid

2000 MATHEMATICS SUBJECT CLASSIFICATION:

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

Acknowledgment

The authors are grateful to the referee for helpful suggestions.