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
- António Almeida Costa, Les $\mu$-demi-anneaux, Séminaire P. Dubreil, 25e année (1971/72), Algèbre, Fasc. 2: Journées d’Algèbre. Journées sur les Anneaux et les Demi-groupes (Paris, 1972), Exp. No. J1, Secrétariat Mathématique, Paris, 1973, pp. 9 (French). MR 0393137 —, $\mu$-systèmes et $\pi$-systèmes d’idéaux, 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 théorie générale des demi-anneaux, Publ. Math. Debrecen 10 (1963), 14–29 (French). MR 168608
- Ma. L. Noronha Galvão, On a Noether-Krull theory for semi-rings, Univ. Lisboa Rev. Fac. Ci. A (2) 8 (1960/61), 175–256 (Portuguese). MR 161892
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