IJPAM: Volume 86, No. 4 (2013)

IDEMPOTENT AND REGULAR GENERALIZED
COHYPERSUBSTITUTIONS OF TYPE $\tau = (2)$

N. Saengsura$^1$, S. Jermjitpornchai
Department of Mathematics
Faculty of Science
Mahasarakham University
Mahasarakham, 44150, THAILAND


Abstract. A mapping $\sigma$ which assigns to every $n_i$-ary cooperation symbol $f_i$ a coterm of type $\tau=(n_i)_{i\in I}$ is said to be a generalized cohypersubstitution of type $\tau$. Every generalized cohypersubstition $\sigma$ of type $\tau$ induces a mapping $\hat{\sigma}$ on the set of all coterms of type $\tau$. The set of all generalized cohypersubstitutions of type $\tau$ under the binary operation $\circ_{CG}$ which is defined by $\sigma_1\circ_{CG}\sigma_2:=\hat{\sigma_1}\circ \sigma_2$ for all $\sigma_1,\sigma_2\in \mathit{Cohyp}_G(\tau)$ forms a monoid which is called the monoid of cohypersubstitution of type $\tau$. In this research, we characterize all idempotent and regular elements of $\mathit{Cohyp(\tau)}$ where $\tau = (2)$.

Received: June 10, 2013

AMS Subject Classification: 20M14, 20F50

Key Words and Phrases: cohypersubstitutions, coterms, superpositions, idempotent elements, regular elements

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DOI: 10.12732/ijpam.v86i4.13 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 86
Issue: 4