Abstract
The direct product R = x i∈ R i of a family of semirings {R i | i ∈ Ω} has the structure of a semiring with the operations of addition and multiplication defined componentwise. This semiring is additively- [resp. multiplicatively-] idempotent [resp. zerosumfree, simple] if each of the R i is additively- [resp. multiplicatively-] idempotent [resp. zerosumfree, simple]. It is not entire if Ω has order greater than 1.
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© 1999 Springer Science+Business Media Dordrecht
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Golan, J.S. (1999). Sets and Relations with Values in a Semiring. In: Semirings and their Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9333-5_2
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DOI: https://doi.org/10.1007/978-94-015-9333-5_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5252-0
Online ISBN: 978-94-015-9333-5
eBook Packages: Springer Book Archive