A note on commutative semigroups

1 November 1968

journal article
research article
Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society

Vol. 8 (4) , 731-736
https://doi.org/10.1017/s1446788700006558

Abstract

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.

Keywords

NOTE
BOOLEAN ALGEBRA
ARBITRARY COMMUTATIVE
COMPLEMENTED SEMILATTICE
PSEUDO COMPLEMENTED
CLOSED ELEMENTS
ELEMENTS FORM
COMMUTATIVE SEMIGROUPS

This publication has 5 references indexed in Scilit:

The Space of Minimal Prime Ideals of a Commutative Ring
Transactions of the American Mathematical Society, 1965
Minimal Prime Ideals in Commutative Semigroups
Proceedings of the London Mathematical Society, 1963
Pseudo-complements in semi-lattices
Duke Mathematical Journal, 1962
Homorphisms of Semi-Groups
Annals of Mathematics, 1954
Representations of Boolean algebras
Bulletin of the American Mathematical Society, 1941