Green's-Like Relations on Algebras and Varieties
Joint Authors
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2008, Issue 2008 (31 Dec. 2008), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2007-11-26
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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 type τ.
Some sort of (super-)associativity is needed for such definitions to work, and we consider algebras which are clones of terms of type τ, where the clone axioms including superassociativity hold.
This allows us to define for any variety V of type τ two Green's-like relations ℒV and ℛV on the term clone of type τ.
We prove a number of properties of these two relations, and describe their behaviour when V is a variety of semigroups.
American Psychological Association (APA)
Denecke, K.& Wismath, S. L.. 2007. Green's-Like Relations on Algebras and Varieties. International Journal of Mathematics and Mathematical Sciences،Vol. 2008, no. 2008, pp.1-13.
https://search.emarefa.net/detail/BIM-987886
Modern Language Association (MLA)
Denecke, K.& Wismath, S. L.. Green's-Like Relations on Algebras and Varieties. International Journal of Mathematics and Mathematical Sciences No. 2008 (2008), pp.1-13.
https://search.emarefa.net/detail/BIM-987886
American Medical Association (AMA)
Denecke, K.& Wismath, S. L.. Green's-Like Relations on Algebras and Varieties. International Journal of Mathematics and Mathematical Sciences. 2007. Vol. 2008, no. 2008, pp.1-13.
https://search.emarefa.net/detail/BIM-987886
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-987886