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A Semigroup Approach to Lattices

Published online by Cambridge University Press:  20 November 2018

M. F. Janowitz
M. F. Janowitz*
Affiliation:
University of New Mexico
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In (3, p. 85) we denned a Baer semigroup to be a multiplicative semigroup with 0 having the property that the left (right) annihilator of every element is a principal left (right) ideal generated by an idempotent. We showed (3, Lemma 1(vi) and Theorem 5, p. 86) that with set inclusion as the partial order, the set of left annihilators and the set of right annihilators of elements of a Baer semigroup form dual isomorphic lattices with 0 and 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 1212 - 1223
Copyright
Copyright © Canadian Mathematical Society 1966

References

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3. Janowitz, M. F., Boer semigroups, Duke Math. J., 32 (1965), 85–95.Google Scholar
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