The $k$-closure of monic and monic free ideals in a polynomial semiring
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- by Louis Dale
- Proc. Amer. Math. Soc. 64 (1977), 219-226
- DOI: https://doi.org/10.1090/S0002-9939-1977-0444717-9
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Abstract:
The concepts of k-closure, k-boundary and weak k-ideals are introduced and necessary and sufficient conditions that an ideal be a k-ideal are given. These conditions are applied to monic and monic free k-ideals. Also, it is shown that the ascending chain condition holds for monic ideals, but not for monic free ideals, and that a semiring S is Noetherian if and only if $S[x]$ satisfies the ascending chain condition for monic ideals.References
- Louis Dale, Monic and monic free ideals in a polynomial semiring, Proc. Amer. Math. Soc. 56 (1976), 45–50. MR 404354, DOI 10.1090/S0002-9939-1976-0404354-8
- Paul J. Allen and Louis Dale, Ideal theory in the semiring $Z^{+}$, Publ. Math. Debrecen 22 (1975), no. 3-4, 219–224. MR 404352, DOI 10.5486/pmd.1975.22.3-4.07
- 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
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 64 (1977), 219-226
- MSC: Primary 16A78
- DOI: https://doi.org/10.1090/S0002-9939-1977-0444717-9
- MathSciNet review: 0444717