Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-17T06:55:06.276Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on commutative semigroups

Published online by Cambridge University Press:  09 April 2009

T. P. Speed
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 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
[4]Kist, J., ‘Minimal prime ideals in commutative semi-groups’, Proc. Lond. Math. Soc. Ser. 3. xiii (1963), 31–50.CrossRefGoogle Scholar
[5]Pierce, R. S., ‘Homomorphisms of semi-groups’, Ann. Math. 59 (1954), 287–291.CrossRefGoogle Scholar
[6]Sikorski, R., Boolean algebras (2nd Edition, Springer-Verlag 1964).Google Scholar