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BIBTEX RIS

On Croisot’s theory of decompositions

1969; Mathematical Sciences Publishers; Volume: 28; Issue: 1 Linguagem: Inglês

10.2140/pjm.1969.28.105

ISSN

1945-5844

Autores

Kenneth M. Kapp,

Tópico(s)

Logic, programming, and type systems

Resumo

Croisot gave a definition of (m, w)-regularity which he then showed defined four logically distinct classes of semi-groups.However, semigroups with nilpotent elements did not fall within his classification.Our generalization of (m, n)°-regularity remedies this exclusion; countably many distinct classes of semi-groups are defined.In particular we investigate the structure of semigroups which are (2, 2)°-regular.We show that a semigroup S is in this class precisely when for each xeS either x 2 = 0 or x 2 e H x .Further, each regular £& -class together with 0 of such a semigroup is itself a completely 0-simple semigroup.The (2, 2)°regularity condition is specialized to that of absorbency: for each a,beS either ab = 0 or abe(R a n L b ).We show that a regular absorbent semigroup is just a mutually annihilating collection of completely 0-simple semigroups.

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