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A note on commutative semigroups

Published online by Cambridge University Press:  09 April 2009

T. P. Speed
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In 1962, O. Frink [2] showed that in a pseudo-complemented semilattice 〈P; ∧, *, 0〉, the closed elements form a Boolean algebra. We shall consider an extension of this result to arbitrary commutative semigroups with zero.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 4 , November 1968 , pp. 731 - 736
Copyright
Copyright © Australian Mathematical Society 1968

References

[1]Frink, O., ‘Representations of Boolean algebras’, Bull. Amer. Math. Soc. 47 (1941), 755–756.CrossRefGoogle Scholar
[2]Frink, O., ‘Pseudo-complements in semi-lattices’, Duke Math. Journ. 29 (1962), 505–513.CrossRefGoogle Scholar
[3]Henriksen, M. & Jerison, M., ‘The space of minimal prime ideals of a commutative ring’, Trans. Amer. Math. Soc. 115 (1965), 110–130.CrossRefGoogle Scholar
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[6]Sikorski, R., Boolean algebras (2nd Edition, Springer-Verlag 1964).Google Scholar