Ideals in Semirings

Jonathan S. Golan
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Jonathan S. Golan: University of Haifa

Chapter 6 in Semirings and their Applications, 1999, pp 65-83 from Springer

Abstract: Abstract Ideals play a fundamental role in ring theory and it is therefore natural to consider them also in the context of semiring theory. Here their role is no less important, though we will often have to restrict our consideration to special types of ideals. In particular, we will show that, as in the case of rings, the family of all ideals of a semiring is, in a natural way, a semiring. Formally, the definitions in the two situations are the same.

Keywords: Maximal Ideal; Nonempty Subset; Left Ideal; Multiplicative Identity; Minimal Left Ideal (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-94-015-9333-5_6

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