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A note on the coordinatisation of implicative (semi-)lattices by Baer semigroups

Published online by Cambridge University Press:  14 November 2011

C. S. Johnson Jr.
C. S. Johnson Jr.
Affiliation:
Bowling Green State University, Ohio, U.S.A.
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Synopsis

We show that a bounded (semi-)lattice is implicative if and only if it can be coordinatised by a (right) Baer semigroup ℛS in which each element of (S) has an idempotent generator f such that fe = efe for all idempotents e with eS ∈ ℛ(S).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 82 , Issue 1-2 , 1978 , pp. 115 - 116
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

1Blyth, T. S.. A coordinatisation of implicative (semi-) lattices by Baer semigroups. Proc. Roy. Soc. Edinburgh Sect. A 82 (1978), 111–113.Google Scholar
2Janowitz, M. F.. Semimultiplicative residuated mappings. Algebra Universalis 5 (1975), 429–442.Google Scholar
3Johnson, C. S. Jr, UIG Baer semigroups. J. Natur. Sci. and Math. 12 (1972), 287–295.Google Scholar