Displaying similar documents to “Arithmetic functions over rings with zero divisors.”

Atomicity and the fixed divisor in certain pullback constructions

Jason Greene Boynton (2012)

Colloquium Mathematicae

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Let D be an integral domain with field of fractions K. In this article, we use a certain pullback construction in the spirit of Int(E,D) that furnishes many examples of domains between D[x] and K[x] in which there are elements that do not admit a finite factorization into irreducible elements. We also define the notion of a fixed divisor for this pullback construction to characterize all of its irreducible elements and those nonzero nonunits that do admit a finite factorization into...

Chain conditions on composite Hurwitz series rings

Jung Wook Lim, Dong Yeol Oh (2017)

Open Mathematics

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In this paper, we study chain conditions on composite Hurwitz series rings and composite Hurwitz polynomial rings. More precisely, we characterize when composite Hurwitz series rings and composite Hurwitz polynomial rings are Noetherian, S-Noetherian or satisfy the ascending chain condition on principal ideals.

Boundary map and overrings of half-factorial domains

Nathalie Gonzalez, Sébastien Pellerin (2005)

Bollettino dell'Unione Matematica Italiana

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We investigate factorization of elements in overrings of a half-factorial domain A in relation with the behaviour of the boundary map of A . It turns out that a condition, called C ⋆ , on the extension plays a central role in this study. We finally apply our results to the special case of A + X ⁢ B ⁢ X polynomial rings.