The Translational Hull of the Rees Matrix Semigroup over the Strong Semilattice of Monoids
Zhou Yong-an · Shuxue de shijian yu renshi · 2012
Let A be a monoid and A be the semilattice of monoids {A_e} with the identity of A is 1_a and the identity of A_e is e.Let E(A)be the set of all the identities e of A_e.Let S be the Rees semigroup over A and S_e be the Rees semigroup over A_e.Then the the following five conditions axe equivalent:(1)For all e∈E(A),a∈A,ae = ea;(2)A is the strong semilattice of the monoids {A_e};(3)S is the strong semilattice of {S_e};(4)The translationsl hull of A and the strong semilattice of the translational hulls of {A_e} are isomorphic;(5)The translational hull of S and the strong semilattice of the translational hulls of {S_e} are isomorphic.