Bounded Factorization and the Ascending Chain Condition on Principal Ideals in Generalized Power Series Rings

H. E. Bruch (), J. R. Juett () and Christopher Park Mooney ()
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H. E. Bruch: Goodwill Excel Center
J. R. Juett: University of Dubuque
Christopher Park Mooney: University of Wisconsin-Stout

A chapter in Algebraic, Number Theoretic, and Topological Aspects of Ring Theory, 2023, pp 135-153 from Springer

Abstract: Abstract We determine necessary and sufficient conditions for broad classes of generalized power series rings to satisfy the ascending chain condition on principal ideals or possess the bounded factorization property. Along the way, we consider when a generalized power series ring is domainlike or (weakly) présimplifiable. As corollaries to our general theorems, we derive new factorization-theoretic results about (Laurent) power series rings and the “large polynomial rings” of Halter-Koch.

Keywords: Bounded factorization ring; Ascending chain condition on principal ideals; Generalized power series ring; (Weakly) présimplifiable ring; Domainlike ring; 13F15; 13A05; 13F25; 20M25 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-28847-0_9

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DOI: 10.1007/978-3-031-28847-0_9

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