All Regular Elements in HypG(2)

• Journal title : Kyungpook mathematical journal
• Volume 51, Issue 2,  2011, pp.139-143
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2011.51.2.139
Title & Authors
All Regular Elements in HypG(2)
Puninagool, Wattapong; Leeratanavalee, Sorasak;

Abstract
In this paper we consider mappings $\small{{\sigma}}$ which map the binary operation symbol f to the term $\small{{\sigma}}$(f) which do not necessarily preserve the arities. We call these mappings generalized hypersubstitutions. Any generalized hypersubstitution $\small{{\sigma}}$ can be extended to a mapping $\small{\hat{\sigma}}$ on the set of all terms of type $\small{{\tau}}$ = (2). We de ne a binary operation on the set $\small{Hyp_G}$(2) of all generalized hypersubstitutions of type $\small{{\tau}}$ = (2) by using this extension The set $\small{Hyp_G}$(2) together with the identity generalized hypersubstitution $\small{{\sigma}_{id}}$ which maps f to the term f($\small{x_1,x_2}$) forms a monoid. We determine all regular elements of this monoid.
Keywords
generalized hypersubstitution;regular elements;
Language
English
Cited by
1.
NATURAL PARTIAL ORDERING ON E(HypG(2)), Asian-European Journal of Mathematics, 2013, 06, 02, 1350016
2.
The Relationship between Some Regular Subsemigroups ofHypG2, Journal of Mathematics, 2014, 2014, 1
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