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

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Algebraic, Number Theoretic, and Topological Aspects of Ring Theory

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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.

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Acknowledgements

On the occasion of Professor Dan Anderson’s retirement, we would like to acknowledge the mentorship that he has provided us and many others throughout his career. We would also like to acknowledge the anonymous referee for carefully reading our manuscript and offering several corrections/clarifications to our writing.

Author information

Authors and Affiliations

  1. Goodwill Excel Center, Lockhart, TX, USA

    H. E. Bruch

  2. University of Dubuque, Dubuque, IA, USA

    J. R. Juett

  3. University of Wisconsin-Stout, Menomonie, WI, USA

    Christopher Park Mooney

Authors
  1. H. E. Bruch
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  2. J. R. Juett
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  3. Christopher Park Mooney
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Corresponding author

Correspondence to Christopher Park Mooney .

Editor information

Editors and Affiliations

  1. Département de Mathématiques, Université de Picardie, Amiens, France

    Jean-Luc Chabert

  2. Università degli Studi Roma Tre, Dipartimento di Matematica e Fisica, Rome, Italy

    Marco Fontana

  3. Institut für Analysis und Zahlentheorie, Technische Universität Graz, Graz, Austria

    Sophie Frisch

  4. Department of Mathematics, University of Connecticut, Storrs, CT, USA

    Sarah Glaz

  5. Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada

    Keith Johnson

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Bruch, H.E., Juett, J.R., Mooney, C.P. (2023). Bounded Factorization and the Ascending Chain Condition on Principal Ideals in Generalized Power Series Rings. In: Chabert, JL., Fontana, M., Frisch, S., Glaz, S., Johnson, K. (eds) Algebraic, Number Theoretic, and Topological Aspects of Ring Theory . Springer, Cham. https://doi.org/10.1007/978-3-031-28847-0_9

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