Arithmetic of Semigroup Semirings
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We define semigroup semirings by analogy with group rings and semigroup rings. We study the arithmetic properties and determine sufficient conditions under which a semigroup semiring is atomic, has finite factorization, or has bounded factorization. We also present a semigroup-semiring analog (although not a generalization) of the Gauss lemma on primitive polynomials.
KeywordsGroup Ring Semigroup Forum Unique Factorization Great Common Divisor Commutative Semigroup
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