The -closure of monic and monic free ideals in a polynomial semiring
Proc. Amer. Math. Soc. 64 (1977), 219-226
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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 satisfies the ascending chain condition for monic ideals.
Dale, Monic and monic free ideals in a
polynomial semiring, Proc. Amer. Math. Soc.
56 (1976), 45–50.
0404354 (53 #8156), http://dx.doi.org/10.1090/S0002-9939-1976-0404354-8
J. Allen and Louis
Dale, Ideal theory in the semiring 𝑍⁺, Publ.
Math. Debrecen 22 (1975), no. 3-4, 219–224. MR 0404352
J. Allen, A fundamental theorem of homomorphisms
for semirings, Proc. Amer. Math. Soc. 21 (1969), 412–416.
0237575 (38 #5856), http://dx.doi.org/10.1090/S0002-9939-1969-0237575-4
- L. Dale, Monic and monic free ideals in a polynomial semiring, Proc. Amer. Math. Soc. 56 (1976), 45-50. MR 0404354 (53:8156)
- L. Dale and P. J. Allen, Ideal theory in the semiring , Publ. Math. Debrecen 22 (1975), 219-224. MR 0404352 (53:8154)
- P. J. Allen, A fundamental theorem of homomorphisms for semirings, Proc. Amer. Math. Soc. 21 (1969), 412-416. MR 0237575 (38:5856)
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