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Principal-like ideals and related polynomial content conditions

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Commutative Algebra

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Abstract

We discuss several classes of ideals (resp., modules) having properties shared by principal ideals (resp., cyclic modules). These include multiplication ideals and modules and cancellation ideals and modules. We also discuss polynomial content conditions including Gaussian ideals and rings and Armendariz rings.

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Authors and Affiliations

  1. University of Iowa, Iowa City, IA, 52242, USA

    D. D. Anderson

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  1. D. D. Anderson
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Correspondence to D. D. Anderson .

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Editors and Affiliations

  1. , Dipartimento di Matematica, Università degli Studi Roma Tre, Largo San Leonardo Murialdo 1, Roma, 00146, Italy

    Marco Fontana

  2. , Department of Mathematics and Statistics, King Fahd University of Petroleum & Mine, Dhahran, 31261, Saudi Arabia

    Salah-Eddine Kabbaj

  3. , Department of Mathematical Sciences, New Mexico State University, Las Cruces, 88003, New Mexico, USA

    Bruce Olberding

  4. , Department of Mathematics, Reed College, Southeast Woodstock Blvd. 3203, Portland, 97202-8199, Oregon, USA

    Irena Swanson

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Dedicated to the memory of my teacher, Irving Kaplansky, who piqued my interest in these topics.

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Anderson, D.D. (2011). Principal-like ideals and related polynomial content conditions. In: Fontana, M., Kabbaj, SE., Olberding, B., Swanson, I. (eds) Commutative Algebra. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6990-3_1

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