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Noetherian Semigroup Algebras and Beyond

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Multiplicative Ideal Theory and Factorization Theory

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 170))

Abstract

A selection of results on Noetherian semigroup algebras is presented. They are of structural, arithmetical, and combinatorial nature. Starting with the case of Noetherian group algebras, where several deep results are known, a lot of attention is later given to the case of algebras of submonoids of groups. The role of algebras of this type in the general theory of Noetherian semigroup algebras is explained and sample structural results on arbitrary Noetherian semigroup algebras, based on this approach, are presented. A special emphasis is on various classes of algebras with good arithmetical properties, such as maximal orders and principal ideal rings. In this context, several results indicating the nature and applications of the structure of prime ideals are presented. Recent results on the prime spectrum and arithmetics of a class of non-Noetherian orders are also given.

Research supported by the National Science Centre grant 2013/09/B/ST1/04408.

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Authors and Affiliations

  1. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Jan Okniński

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  1. Jan Okniński
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Correspondence to Jan Okniński .

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Editors and Affiliations

  1. Dept of Math & Stat, Sam Houston State University, Huntsville, Texas, USA

    Scott Chapman

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

    Marco Fontana

  3. Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz, Graz, Austria

    Alfred Geroldinger

  4. Dept. Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico, USA

    Bruce Olberding

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Okniński, J. (2016). Noetherian Semigroup Algebras and Beyond. In: Chapman, S., Fontana, M., Geroldinger, A., Olberding, B. (eds) Multiplicative Ideal Theory and Factorization Theory. Springer Proceedings in Mathematics & Statistics, vol 170. Springer, Cham. https://doi.org/10.1007/978-3-319-38855-7_11

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