Abstract:An analogue for halfrings of the Hilbert Basis Theorem is obtained by a study of the relationship between the ideals of a halfring and the ideals of its ring of differences. This technique also results in a characterization of those ideals for which the factor semiring has no nontrivial semi-isomorphic images.
Paul J. Allen, Ideal theory in semirings, Dissertation, Texas Christian University, Fort Worth, Texas, 1967.
- Paul J. Allen, A fundamental theorem of homomorphisms for semirings, Proc. Amer. Math. Soc. 21 (1969), 412–416. MR 237575, DOI 10.1090/S0002-9939-1969-0237575-4
- Samuel Bourne, On the homomorphism theorem for semirings, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 118–119. MR 45693, DOI 10.1073/pnas.38.2.118 M. Henriksen, Ideals in semirings with commutative addition, Notices Amer. Math. Soc. 5 (1958), 321. Abstract #542-183.
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 8-14
- MSC: Primary 16A78
- DOI: https://doi.org/10.1090/S0002-9939-1972-0291228-5
- MathSciNet review: 0291228