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|Homomorphisms; fundamental inverse semigroups Let S be an inverse |
semigroup, let T be a semigroup and let 9: S + T ... Clifford semigroups An
inverse semigroup S is called a Cliffbrd semigroup if and only if every idempotent
of S is central.
|D Lemma 15.9 () A semigroup S is regular and satisfies a permutation identity |
sis2 ...sn = а<т(1)s<т(2) . . . з„(n) for some a £ Sn (n > 2) with cr(1) ^ 1, a(n) ф n if
and only if S is a commutative Clifford semigroup. Proof. Let 5 be a regular ...
|AMS 1980 Subject Classification: 53A35 CLIFFORD SEMI-GROUP, completely-|
regular semigroup - A semi-group in which every element is a group element,
that is, lies in some subgroup. An element of a semi-group is a group element if
|Even the reassembly of a commutative semigroup from its archimedean |
components seems quite difficult, and has been solved only in highly particular
cases: when the archimedean components are groups (Clifford ),
|This paper investigates ring-theoretic properties of a Noetherian domain that |
reflect reciprocally in the Clifford or Boolean property of its t-class semigroup.
Keywords. Class semigroup, t-class semigroup, t-ideal, t-closure, Clifford
|We now have the following; it tells us, in a general way, how to construct inverse |
semigroups from Clifford semigroups and fuundamental semigroups. Theorem 7
Every inverse semigroup can be embedded in a \-semidirect product of a Clifford
|of the term 'non-singular', he defined a finite simple or 0-simple semigroup to be c|
-non-singular if it is isomorphic to a Rees matrix ... a group: it necessarily
coincides with its own structure group (see Clifford and Preston 1961, Corollary
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