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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Ordered power associative groupoids


Author: Desmond A. Robbie
Journal: Proc. Amer. Math. Soc. 31 (1972), 285-290
DOI: https://doi.org/10.1090/S0002-9939-1972-0285662-7
MathSciNet review: 0285662
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Abstract | References | Additional Information

Abstract: Compact, connected, totally ordered, (Hausdorff) topological groupoids, with restrictions on their sets of idempotents and with varying degrees of power associativity assumed, are examined. The paper evolves from the author's example of such a groupoid which has only two idempotents (a zero for least element, and an identity for greatest element), a compact neighborhood of the greatest element consisting of power associative elements, and which is not isomorphic to either the real thread or the nil thread. Another example given has a zero for least element, an idempotent for greatest element, and no other idempotents, and has a compact neighborhood of the greatest element consisting of an associative subgroupoid in which all products are equal to the greatest element. Theorems are given which show that these examples, and one other, in some sense, exhaust the possibilities.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0285662-7
Keywords: Ordered groupoid, power associative, sect, cancellative, real thread, nil thread, isomorphism
Article copyright: © Copyright 1972 American Mathematical Society