1. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 17. 18. © T-Class Semigroups Of Integral Domains Kabbaj, S; Mimouni, A WALTER DE GRUYTER CO, JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK; pp: 213-229; Vol: 612 King Fahd University of Petroleum & Minerals http://www.kfupm.edu.sa Summary 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 nu-multiplication domain (PVMD) is of Krull type (in the sense of Griffin [24]) if and only if its t-class semigroup is Clifford. This extends Bazzoni and Salce's results on valuation domains [11] and Prufer domains [7], [8], [9], [10]. References: ANDERSON DD, 1987, HOUSTON J MATH, V13, P13 ANDERSON DD, 1991, J ALGEBRA, V142, P285 ANDERSON DF, 1980, CAN J MATH, V32, P362 ANDERSON DF, 1991, CAN MATH BULL, V34, P15 BARUCCI V, 1986, J ALGEBRA, V99, P132 BASTIDA E, 1973, MICH MATH J, V20, P79 BAZZONI S, 1996, ISRAEL J MATH, V95, P135 BAZZONI S, 1996, J ALGEBRA, V184, P613 BAZZONI S, 1998, LECT NOTES PURE APPL, V201, P79 BAZZONI S, 2000, COMMUN ALGEBRA, V28, P5157 BAZZONI S, 2001, J ALGEBRA, V238, P703 BREWER JW, 1976, MICH MATH J, V23, P33 DOBBS DE, 1976, PROC AMER MATH SOC, V56, P51 DOBBS DE, 1989, COMMUN ALGEBRA, V17, P2835 ELBAGHDADI S, 2002, COMMUN ALGEBRA, V30, P3723, DOI 16.10.1081/AGB-120005815 FANGGUI W, 1999, J PURE APPL ALGEBRA, V135, P155 FONTANA M, 1993, J ALGEBRA, V157, P489 Copyright: King Fahd University of Petroleum & Minerals; http://www.kfupm.edu.sa

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