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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A characterization of $\mu$-semirings
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by Margarita Ramalho PDF
Proc. Amer. Math. Soc. 60 (1976), 49-52 Request permission

Abstract:

A characterization of $\mu$-semirings is given, namely, “A semiring $\mathfrak {S}$ is a $\mu$-semiring, if and only if, for each ideal $\mathfrak {a}$ of $\mathfrak {S}$ with no subideals in a $\pi$-system $\mathfrak {B}$, there exists a maximal ideal which has no subideals in $\mathfrak {B}$ and contains $\mathfrak {a}$."
References
  • AntĂłnio Almeida Costa, Les $\mu$-demi-anneaux, SĂ©minaire P. Dubreil, 25e annĂ©e (1971/72), Algèbre, Fasc. 2: JournĂ©es d’Algèbre. JournĂ©es sur les Anneaux et les Demi-groupes (Paris, 1972), Exp. No. J1, SecrĂ©tariat MathĂ©matique, Paris, 1973, pp. 9 (French). MR 0393137
  • —, $\mu$-systèmes et $\pi$-systèmes d’idĂ©aux, Univ. Lisboa Revista Fac. Ci. 7 (1959), 235-243.
  • A. Almeida Costa, Sur les $\mu$-demi-anneaux, Math. Z. 108 (1968), 10–14 (French). MR 237576, DOI 10.1007/BF01110452
  • A. Almeida Costa, Sur la thĂ©orie gĂ©nĂ©rale des demi-anneaux, Publ. Math. Debrecen 10 (1963), 14–29 (French). MR 168608
  • Ma. L. Noronha GalvĂŁo, On a Noether-Krull theory for semi-rings, Univ. Lisboa Rev. Fac. Ci. A (2) 8 (1960/61), 175–256 (Portuguese). MR 161892
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 49-52
  • MSC: Primary 16A78
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0419538-2
  • MathSciNet review: 0419538