Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Ordered power associative groupoids
HTML articles powered by AMS MathViewer

by Desmond A. Robbie PDF
Proc. Amer. Math. Soc. 31 (1972), 285-290 Request permission

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.
References
  • J. Aczél, Quasigroups, nets, and nomograms, Advances in Math. 1 (1965), no. fasc. 3, 383–450. MR 193174, DOI 10.1016/0001-8708(65)90042-3
  • L. Fuchs, Partially ordered algebraic systems, Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1963. MR 0171864
  • John G. Hocking and Gail S. Young, Topology, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1961. MR 0125557
  • K. H. Hofmann, Zur mathematischen Theorie des Messens, Rozprawy Mat. 32 (1963), 32 (German). MR 195070
  • Karl Heinrich Hofmann and Paul S. Mostert, Elements of compact semigroups, Charles E. Merrill Books, Inc., Columbus, Ohio, 1966. MR 0209387
  • R. J. Koch and A. D. Wallace, Maximal ideals in compact semigroups, Duke Math. J. 21 (1954), 681–685. MR 63381
    • P. S. Mostert, Comments on a paper of Warne, Mimeographed sheets, Tulane University, New Orleans, La., 1963. D. A. Robbie, Some theorems on binary topological algebras, Dissertation, University of Florida, Gainesville, Fla., 1970.
  • Kermit Sigmon, Cancellative medial means are arithmetic, Duke Math. J. 37 (1970), 439–445. MR 274644
  • R. J. Warne, Connected ordered topological groupoids with idempotent endpoints, Publ. Math. Debrecen 8 (1961), 143–146. MR 130678
  • Raymond Louis Wilder, Topology of Manifolds, American Mathematical Society Colloquium Publications, Vol. 32, American Mathematical Society, New York, N. Y., 1949. MR 0029491
Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 31 (1972), 285-290
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0285662-7
  • MathSciNet review: 0285662