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Ideal types in a polynomial halfring


Author: Louis Dale
Journal: Proc. Amer. Math. Soc. 75 (1979), 189-195
MSC: Primary 16A78
DOI: https://doi.org/10.1090/S0002-9939-1979-0532133-2
MathSciNet review: 532133
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Abstract: Ideal types are used to classify ideals in a polynomial halfring and to determine when an ideal behaves like a k-ideal. In particular, these results are used to classify all ideals in the ring of polynomials over the integers.


References [Enhancements On Off] (What's this?)

  • [1] L. Dale, The k-closure of monic and monic free ideals in a polynomial semiring, Proc. Amer. Math. Soc. 64 (1977), 219-226. MR 0444717 (56:3067)
  • [2] -, Monic and monic free ideals in a polynomaial semiring, Proc. Amer. Math. Soc. 56 (1976), 45-50. MR 0404354 (53:8156)
  • [3] L. Dale and P. J. Allen, Ideal theory in the semiring $ {Z^ + }$, Publ. Math. Debrecen 22 (1975), 219-224. MR 0404352 (53:8154)
  • [4] H. Stone, Ideals in halfrings, Proc. Amer. Math. Soc. 33 (1972), 8-14. MR 0291228 (45:322)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0532133-2
Keywords: Semiring, halfring, ideal type, monotypic, k-ideal, weak k-ideal, k-closure
Article copyright: © Copyright 1979 American Mathematical Society

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