All Regular Elements in HypG(2)

Puninagool, Wattapong;Leeratanavalee, Sorasak

  • Received : 2010.08.17
  • Accepted : 2010.09.27
  • Published : 2011.06.30


In this paper we consider mappings ${\sigma}$ which map the binary operation symbol f to the term ${\sigma}$(f) which do not necessarily preserve the arities. We call these mappings generalized hypersubstitutions. Any generalized hypersubstitution ${\sigma}$ can be extended to a mapping $\hat{\sigma}$ on the set of all terms of type ${\tau}$ = (2). We de ne a binary operation on the set $Hyp_G$(2) of all generalized hypersubstitutions of type ${\tau}$ = (2) by using this extension The set $Hyp_G$(2) together with the identity generalized hypersubstitution ${\sigma}_{id}$ which maps f to the term f($x_1,x_2$) forms a monoid. We determine all regular elements of this monoid.


generalized hypersubstitution;regular elements


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