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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Structure mappings, coextensions and regular four-spiral semigroups

Author: John Meakin
Journal: Trans. Amer. Math. Soc. 255 (1979), 111-134
MSC: Primary 20M10
MathSciNet review: 542873
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Abstract: The structure mapping approach to regular semigroups developed by K. S. S. Nambooripad and J. Meakin is used to describe the $\mathcal {K}$-coextensions of the fundamental four-sprial semigroup and hence to describe the structure of all regular semigroups whose idempotents form a four-spiral biordered set. Isomorphisms between regular four-spiral semigroups are studied. The notion of structural uniformity of a regular semigroup is defined and exploited.

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Keywords: Regular semigroup, structure mappings, <!– MATH $\mathcal {K}$ –> <IMG WIDTH="21" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\mathcal {K}$">-coextensions, structural uniformity, four-spiral semigroup, biordered set, bisimple <IMG WIDTH="19" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img4.gif" ALT="$\omega$">-semigroup, trace, Rees groupoid, natural partial order on a regular semigroup, pseudo-semilattice, pseudo-inverse semigroup
Article copyright: © Copyright 1979 American Mathematical Society