t-Class Semigroups of Integral Domains
| dc.creator | Kabbaj, S. | |
| dc.creator | Mimouni, A. | |
| dc.date | 2006-06-25 | |
| dc.date | 2007-09-12 | |
| dc.date.accessioned | 2026-07-07T08:29:25Z | |
| dc.date.available | 2026-07-07T08:29:25Z | |
| dc.description | The t-class semigroup of an integral domain is the semigroup of the isomorphy classes of the t-ideals with the operation induced by ideal t-multiplication. This paper investigates ring-theoretic properties of an integral domain that reflect reciprocally in the Clifford or Boolean property of its t-class semigroup. Contexts (including Lipman and Sally-Vasconcelos stability) that suit best t-multiplication are studied in an attempt to generalize well-known developments on class semigroups. We prove that a Prufer v-multiplication domain (PVMD) is of Krull type (in the sense of Griffin) if and only if its t-class semigroup is Clifford. This extends Bazzoni and Salce's results on valuation domains and Prufer domains. We also characterize GCD domains with Boolean t-class semigroup, recovering thus recent results on Bezout domains. | |
| dc.description | Section 4 was removed. J. Reine Angew. Math. (to appear), 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0606636 | |
| dc.identifier | http://arxiv.org/abs/math/0606636 | |
| dc.identifier | J. Reine Angew. Math. 612 (2007) 213-229 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137959 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Number Theory | |
| dc.subject | 13C20; 13F05; 11R65; 11R29; 20M14 | |
| dc.title | t-Class Semigroups of Integral Domains | |
| dc.type | text |