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Reflexive Homomorphic Relations

Published online by Cambridge University Press:  20 November 2018

G. D. Findlay*
Affiliation:
McGill University
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It is well known that a symmetric and transitive relation on a set is reflexive wherever it is defined. In this note we show that a converse is true for homomorphic relations in certain classes of algebras.

Consider a class of similar algebras which contains the sub-algebras and quotient algebras of each of its members. Assume also that the direct product A x B of each pair A, B in is also an algebra belonging to . The algebras of , being similar, have the same set of operations. We observe that other operations, called compound operations, may be obtained by composition from the assigned operations.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1960

References

1. Lambek, J., Goursat's theorem and the Zassenhaus lemma, Canad. J. Math. 10 (1957), 45-56.Google Scholar