Monic and monic free ideals in a polynomial semiring in several variables
Abstract: The study of monic and monic free ideals in a polynomial semiring , where is a commutative semiring with an identity, is extended to . Structure theorems are given for monic, monic free, and monic free -ideals in . It is shown that each monic free -ideal in a strict semiring, is the sum of a finite number of ideals such that each is the union of a proper infinite ascending chain of ideals.
-  Louis Dale, Monic and monic free ideals in a polynomial semiring, Proc. Amer. Math. Soc. 56 (1976), 45–50. MR 0404354, https://doi.org/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 0237575, https://doi.org/10.1090/S0002-9939-1969-0237575-4
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Keywords: Strict semiring, monic ideals, monic free ideals, -ideals
Article copyright: © Copyright 1976 American Mathematical Society