Some Conditions on Semirings

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

Chapter 4 in Semirings and their Applications, 1999, pp 43-57 from Springer

Abstract: Abstract We usually consider semirings on which some sort of additional conditions have been imposed. Many such conditions were given in Chapter 1 and examples given of semirings which do or do not satisfy them. We now want to consider consequences of imposing some of these conditions on a semiring. In particular we will first look at the condition of being an additively-idempotent semiring and at the stronger condition of being a simple semiring. Then we will consider some weaker versions of the condition that elements have additive or multiplicative inverses. Finally, we will take up a condition which guarantees the existence of “enough” multiplicative units.

Keywords: Commutative Semigroup; Zero Divisor; Multiplicative Inverse; Infinite Element; Bounded Distributive Lattice (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-94-015-9333-5_4

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