Monic and monic free ideals in a polynomial semiring in several variables
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- by Louis Dale PDF
- Proc. Amer. Math. Soc. 61 (1976), 209-216 Request permission
Abstract:
The study of monic and monic free ideals in a polynomial semiring $S[x]$, where $S$ is a commutative semiring with an identity, is extended to $S[{x_1},{x_2}, \ldots ,{x_n}]$. Structure theorems are given for monic, monic free, and monic free $k$-ideals in $S[{x_1},{x_2}, \ldots ,{x_n}]$. It is shown that each monic free $k$-ideal in $S[{x_1}, \ldots ,{x_n}],\;S$ a strict semiring, is the sum of a finite number of ideals ${B_i}$ such that each ${B_i}$ is the union of a proper infinite ascending chain of 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, 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
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 61 (1976), 209-216
- MSC: Primary 16A66
- DOI: https://doi.org/10.1090/S0002-9939-1976-0427383-7
- MathSciNet review: 0427383