The Order of Normal Form Generalized Hypersubstitutions of Type τ = (2)

Sudsanit, Sivaree;Leeratanavalee, Sorasak

  • Received : 2013.09.28
  • Accepted : 2013.04.15
  • Published : 2014.09.23


In 2000, K. Denecke and K. Mahdavi showed that there are many idempotent elements in $Hyp_{N_{\varphi}}(V)$ the set of normal form hypersubstitutions of type ${\tau}=(2)$ which are not idempotent elements in Hyp(2) the set of all hypersubstitutions of type ${\tau}=(2)$. They considered in which varieties, idempotent elements of Hyp(2) are idempotent elements of $Hyp_{N_{\varphi}}(V)$. In this paper, we study the similar problems on the set of all generalized hypersubstitutions of type ${\tau}=(2)$ and the set of all normal form generalize hypersubstitutions of type ${\tau}=(2)$ and determine the order of normal form generalize hypersubstitutions of type ${\tau}=(2)$.


Order;normal form generalized hypersubstitution;idempotent element


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