Integral domains and the IDF property

Gotti, Felix; Zafrullah, Muhammad

doi:10.1016/j.jalgebra.2022.08.034

Cited by 5 publications

(1 citation statement)

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“…Furstenberg domains have been studied by N. Lebowitz-Lockard in [31] in connection with the properties of almost atomicity and quasi-atomicity, which we define in the next two paragraphs. In addition, Furstenberg domains have been recently considered in [28] by the first author and Zafrullah in connection with idf-domains (i.e., integral domains whose elements have only finitely many irreducible divisors up to associates). Finally, Furstenberg domains have been considered in [24,Section 5] by Li and the first author in the context of integer-valued polynomials.…”

Section: Introductionmentioning

confidence: 99%

On the Subatomicity of Polynomial Semidomains

Gotti

Polo

2023

Algebraic, Number Theoretic, and Topological Aspects of Ring Theory

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A semidomain is an additive submonoid of an integral domain that is closed under multiplication and contains the identity element. Although atomicity and divisibility in integral domains have been systematically investigated for more than thirty years, the same aspects in the more general context of semidomains have been considered just recently. Here we study subatomicity in the context of semidomains, focusing on whether certain subatomic properties ascend from a semidomain to its polynomial extension and its Laurent polynomial extension. We investigate factorization and divisibility notions generalizing that of atomicity. First, we consider the Furstenberg property, which is due to P. Clark and motivated by the work of H. Furstenberg on the infinitude of primes. Then we consider the almost atomic and quasi-atomic properties, both introduced by J. G. Boynton and J. Coykendall in their study of divisibility in integral domains.

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Section: Introductionmentioning

confidence: 99%