Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-22T16:03:16.979Z Has data issue: false hasContentIssue false

Embedding problems in semiring theory

Published online by Cambridge University Press:  09 April 2009

Mireille P. Grillet
Affiliation:
Department of Mathematics, Kansas State UniversityManhattan, Kanass 66502 U.S.A.
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.

The main object of this paper is to give various constructions of the universal semiring of a partial semiring and apply them to find conditions for the embedding of partial semirings into semirings.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, vol. 1, 2, (Math. Surveys 7, Amer. Math. Soc., Providence, 1961, 1967).Google Scholar
[2]Grillet, M. P., ‘Embedding of a semiring into a semiring with identity’, Acta Math. Sci. Hungar. 20 (1969), 121128.CrossRefGoogle Scholar
[3]Grillet, M. P., ‘Examples of semirings of endomorphisms of a semigroup’, Austral. J. Math. Soc. 9 (1970), 345349.CrossRefGoogle Scholar
[4]Grillet, M. P., ‘Free semirings over a set’, J. Nat. Scj. Math. (Lahore), 9 (1970), 285291.Google Scholar
[5]Grillet, M. P., ‘Plongement d'un demi-anneau partiel dans un demi-anneau,’ C. R. Acad. Sci. Paris 267 (1968), A 7476.Google Scholar
[6]Grillet, P. A. and Petrich, M., ‘Ideal extensions of semigroups’, Pacific J. Math. 26 (1968), 493508.CrossRefGoogle Scholar
[7]Grillet, P. A., ‘Categories of ideal extensions of a semigroup,’ (to appear).Google Scholar