Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-16T01:19:57.484Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Croisot, R., Applications residuées, Ann. Sci. Ecole Norm. Sup., 73 (1956), 453–474,Google Scholar
2. Foulis, D. J., Conditions for the modularity of an orthomodular lattice, Pacific J. Math., 11 (1961), 889–895.Google Scholar
3. Janowitz, M. F., Boer semigroups, Duke Math. J., 32 (1965), 85–95.Google Scholar
4. Janowitz, M. F., Quasi-orthomodular lattices, UNM Technical Report No. 42 (1963).Google Scholar
5. Maeda, F., Kontinuierliche Geometrien (Berlin, 1958).Google Scholar