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Essential normal and conjugate extensions of inverse semigroups

Published online by Cambridge University Press:  18 May 2009

Francis Pastijn
Francis Pastijn
Affiliation:
Dienst Hogere Meetkunde, Rijksuniversiteit te Gent, Krijgslaan 281, B-9000 Gent, Belguim
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In the following we use the notation and terminology of [6] and [7]. If S is an inverse semigroup, then Es denotes the semilattice of idempotents of S. If a is any element of the inverse semigroup, then a−1 denotes the inverse of a in S. An inverse subsemigroup S of an inverse semigroup S′ is self-conjugate in S′ if for all x ∈ S′,x−1Sx ⊆ S; if this is the case, S′ is called a conjugate extension of S. An inverse subsemigroup S of S′ is said to be a full inverse subsemigroup of S′ if Es = Es′. If S is a full self-conjugate inverse subsemigroup of the inverse semigroup S′, then S is called a normal inverse subsemigroup of S′, or, S′ is called a normal extension of S.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 23 , Issue 2 , July 1982 , pp. 123 - 130
Copyright
Copyright © Glasgow Mathematical Journal Trust 1982

References

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