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Class semigroups and t-class semigroups of integral domains

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Commutative Algebra

Abstract

The class (resp., t-class) semigroup of an integral domain is the semigroup of the isomorphy classes of the nonzero fractional ideals (resp., t-ideals) with the operation induced by ideal (t-) multiplication. This paper surveys recent literature which studies ring-theoretic conditions that reflect reciprocally in the Clifford property of the class (resp., t-class) semigroup. Precisely, it examines integral domains with Clifford class (resp., t-class) semigroup and describes their idempotent elements and the structure of their associated constituent groups.

S. Bazzoni (supported by project PRIN-2007 “Rings, algebras, modules and categories”)

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica Pura e Applicata, Università di Padova, 35121, Padova, Italy

    Silvana Bazzoni

  2. Department of Mathematics and Statistics, KFUPM, Dhahran, 31261, Saudi Arabia

    Salah-Eddine Kabbaj

Authors
  1. Silvana Bazzoni
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  2. Salah-Eddine Kabbaj
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Correspondence to Silvana Bazzoni .

Editor information

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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Bazzoni, S., Kabbaj, SE. (2011). Class semigroups and t-class semigroups of integral domains. 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_3

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