The Identities Satisfied By The Semigroup MP1

In this paper we investigate the semigroup Mp1which is the monoid obtained by adding an identity element to the Ress matrix semigroup where Zp is the cyclic group of prime order p.We give a necessary and sufficient condition of the identities satisfied by the monoid Mp1. That is, an identity u≈u holds in the semigroup Mp1if and only if i(u)=i(u), f(u)=f(u) and for any word w of length two the numbers of occurrences of w in u and in v are congruent modulo p. More show that the monoid Mp1is included in a non-finite based variety of completely regular semigroup.