Clifford semigroups and seminear-rings of endomorphisms

Nicholas David Gilbert, Mohammad Samman

Research output: Contribution to journalArticle

Abstract

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
L, then the endomorphisms of S generate a Clifford semigroup E+(S) whose
underlying semilattice is the set of endomorphisms of L These results con-
tribute to the wider theory of seminear-rings of endomorphisms, since E+(S)
has a natural structure as a distributively generated seminear-ring.
Original languageEnglish
Pages (from-to)110-119
Number of pages10
JournalInternational Electronic Journal of Algebra
Volume7
Publication statusPublished - 2010

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Endomorphisms
Semigroup
Ring
Semilattice

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title = "Clifford semigroups and seminear-rings of endomorphisms",
abstract = "We consider the structure of the semigroup of self-mappings of asemigroup S under pointwise composition, generated by the endomorphismsof S. We show that if S is a Clifford semigroup, with underlying semilatticeL, then the endomorphisms of S generate a Clifford semigroup E+(S) whoseunderlying semilattice is the set of endomorphisms of L These results con-tribute 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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Clifford semigroups and seminear-rings of endomorphisms. / Gilbert, Nicholas David; Samman, Mohammad.

In: International Electronic Journal of Algebra, Vol. 7, 2010, p. 110-119.

Research output: Contribution to journalArticle

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T1 - Clifford semigroups and seminear-rings of endomorphisms

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AU - Samman, Mohammad

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N2 - We consider the structure of the semigroup of self-mappings of asemigroup S under pointwise composition, generated by the endomorphismsof S. We show that if S is a Clifford semigroup, with underlying semilatticeL, then the endomorphisms of S generate a Clifford semigroup E+(S) whoseunderlying semilattice is the set of endomorphisms of L These results con-tribute to the wider theory of seminear-rings of endomorphisms, since E+(S)has a natural structure as a distributively generated seminear-ring.

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

M3 - Article

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