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

In: Algebraic, Number Theoretic, and Topological Aspects of Ring Theory

Author

Listed:
  • H. E. Bruch

    (Goodwill Excel Center)

  • J. R. Juett

    (University of Dubuque)

  • Christopher Park Mooney

    (University of Wisconsin-Stout)

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.

Suggested Citation

  • H. E. Bruch & J. R. Juett & Christopher Park Mooney, 2023. "Bounded Factorization and the Ascending Chain Condition on Principal Ideals in Generalized Power Series Rings," Springer Books, in: Jean-Luc Chabert & Marco Fontana & Sophie Frisch & Sarah Glaz & Keith Johnson (ed.), Algebraic, Number Theoretic, and Topological Aspects of Ring Theory, pages 135-153, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-28847-0_9
    DOI: 10.1007/978-3-031-28847-0_9
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