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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Ideals in halfrings


Author: H. E. Stone
Journal: Proc. Amer. Math. Soc. 33 (1972), 8-14
MSC: Primary 16A78
DOI: https://doi.org/10.1090/S0002-9939-1972-0291228-5
MathSciNet review: 0291228
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Abstract: An analogue for halfrings of the Hilbert Basis Theorem is obtained by a study of the relationship between the ideals of a halfring and the ideals of its ring of differences. This technique also results in a characterization of those ideals for which the factor semiring has no nontrivial semi-isomorphic images.


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

  • [1] Paul J. Allen, Ideal theory in semirings, Dissertation, Texas Christian University, Fort Worth, Texas, 1967.
  • [2] -, A fundamental theorem of homomorphisms for semirings, Proc. Amer. Math. Soc. 21 (1969), 412-416. MR 38 #5856. MR 0237575 (38:5856)
  • [3] S. Bourne, On the homomorphism theorem for semirings, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 118-119. MR 13, 618. MR 0045693 (13:618a)
  • [4] M. Henriksen, Ideals in semirings with commutative addition, Notices Amer. Math. Soc. 5 (1958), 321. Abstract #542-183.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0291228-5
Keywords: Halfring, Noetherian semiring, Hilbert Basis Theorem, semi-isomorphism, fundamental theorem of homomorphisms
Article copyright: © Copyright 1972 American Mathematical Society

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