CLIFFORD SEMIGROUPS AND SEMINEAR-RINGS OF ENDOMORPHISMS

CLIFFORD SEMIGROUPS AND SEMINEAR-RINGS OF ENDOMORPHISMS

We consider the structure of the semigroup of self-mappings of a semigroup S under pointwise composition, generated by the endomorphisms of S. We show that if S is a Clifford semigroup, with underlying semilattice Λ, then the endomorphisms of S generate a Clifford semigroup E+(S) whose underlying semilattice is the set of endomorphisms of Λ. These results contribute to the wider theory of seminear-rings of endomorphisms, since E+(S) has a natural structure as a distributively generated seminear-ring.

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  • School of Mathematical and Computer Sciences & the Maxwell Institute for the Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, U.K. e-mail: N.D.Gilbert@hw.ac.uk Mohammad Samman Department of Mathematics and Statistics King Fahd University of Petroleum & Minerals Box 411, Dhahran 31261, Saudi Arabia e-mail: msamman@kfupm.edu.sa