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A characterization of $\mu$-semirings


Author: Margarita Ramalho
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
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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 [Enhancements On Off] (What's this?)

  • 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.
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  • 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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Article copyright: © Copyright 1976 American Mathematical Society