Abstract
There are five equivalence relations known as Green's relations definable on any semigroup or monoid, that is, on any algebra with a binary operation which is associative. In this paper, we examine whether Green's relations can be defined on algebras of any typeτ. Some sort of (super-)associativity is needed for such definitions to work, and we consider algebras which are clones of terms of typeτ, where the clone axioms including superassociativity hold. This allows us to define for any varietyVof typeτtwo Green's-like relationsℒVandℛVon the term clone of typeτ. We prove a number of properties of these two relations, and describe their behaviour whenVis a variety of semigroups.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Mathematics and Mathematical Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
