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Class semigroups and t-class semigroups of integral domains

In: Commutative Algebra

Author

Listed:
  • Silvana Bazzoni

    (Università di Padova, Dipartimento di Matematica Pura e Applicata)

  • Salah-Eddine Kabbaj

    (KFUPM, Department of Mathematics and Statistics)

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.

Suggested Citation

  • Silvana Bazzoni & Salah-Eddine Kabbaj, 2011. "Class semigroups and t-class semigroups of integral domains," Springer Books, in: Marco Fontana & Salah-Eddine Kabbaj & Bruce Olberding & Irena Swanson (ed.), Commutative Algebra, pages 47-76, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-6990-3_3
    DOI: 10.1007/978-1-4419-6990-3_3
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