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Proceedings of the American Mathematical Society

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

 

 

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}$."


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DOI: https://doi.org/10.1090/S0002-9939-1976-0419538-2
Article copyright: © Copyright 1976 American Mathematical Society