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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.

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On the congruence lattices of unary algebras
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by Joel Berman PDF
Proc. Amer. Math. Soc. 36 (1972), 34-38 Request permission

Abstract:

Characterizations of those unary algebras whose congruence lattices are semimodular or atomic are obtained. Combining these results gives necessary and sufficient conditions for a unary algebra to have a geometric congruence lattice.
References
  • Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
  • George Grätzer, Universal algebra, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1968. MR 0248066
  • J. Johnson and R. L. Seifert, A survey of multiunary algebras, Mimeographed Seminar Notes (R. McKenzie, Director), University of California, Berkeley, Calif., 1967. B. Jónsson, Topics in universal algebra, Lecture Notes, Vanderbilt University, Nashville, Tenn., 1969/70.
  • Richard S. Pierce, Introduction to the theory of abstract algebras, Holt, Rinehart and Winston, New York-Montreal, Que.-London, 1968. MR 0227070
  • Michael Yoeli and Abraham Ginzburg, On homomorphic images of transition graphs, J. Franklin Inst. 278 (1964), 291–296. MR 167975, DOI 10.1016/S0016-0032(64)90583-6
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 36 (1972), 34-38
  • MSC: Primary 08A15
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0309833-6
  • MathSciNet review: 0309833