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An Equational Spectrum Giving Cardinalities of Endomorphism Monoids1

Published online by Cambridge University Press:  20 November 2018

Matthew Gould
Matthew Gould*
Affiliation:
University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
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Abstract

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By determining the spectrum of a particular set of equations of type 〈2, 2, 0, 0,0〉 it is shown that a positive integer n is the cardinality of the endomorphism monoid of a universal algebra of the form if and only if n is square.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 3 , August 1975 , pp. 427 - 429
Copyright
Copyright © Canadian Mathematical Society 1975

Footnotes

(1)

This work was partially supported by a grant from the National Research Council of Canada.

References

1. Evans, T., Products of points—some simple algebras and their identities, Amer. Math. Monthly 74 (1967), 362-372.Google Scholar
2. Gould, M., Endomorphism and automorphism structure of direct squares of universal algebras, Pacific Journal of Mathematics, to appear.Google Scholar