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The Dedekind property for semirings

Published online by Cambridge University Press:  09 April 2009

Bill J. Dulin  and
James R. Mosher
Bill J. Dulin
Affiliation:
Texas A&M University College Station, Texas 77843, U.S.A.
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In this article the concept of Dedekind semidomain is defined, and it is shown that certain structures of this kind are Noetherian, have integral closure, and have the property that their prime k-ideals are maximal. The second section provides the appropriate transportation theorems, while the third gives the main result concerning Dedekind semidomains. Examples are given throughout the paper to show that the hypothesies of certain theorems in the paper cannot be greatly weakened.

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 1 , July 1972 , pp. 82 - 90
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Bourne, S., ‘The Jacobson radical of a semiring’, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 163–170.CrossRefGoogle ScholarPubMed
[2]LaTorre, D., ‘On h-ideals and k-ideals in hemirings’, Publ. Math. Debrecen, 12 (1965), 219–226.CrossRefGoogle Scholar
[3]Mosher, J., ‘Generalized quotients of hemirings’, Comp. Math. 22 (1970), 275–281.Google Scholar
[4]Mosher, J., Generalized semirings of quotients, Dissertation (Texas Christian University, 1968).Google Scholar
[5]Stone, H. E., Structure theory of semirings, Dissertation, (Texas Christian University, 1969).Google Scholar
[6]Zariski, O. and Samuel, P., Commutative Algebra, Vol. 1 (Princeton, D. Van Nostrand, 1959).Google Scholar