Star stability and star regularity for Mori domains

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1. [1] V. Barucci, Mori domains, Non-Noetherian Commutative Ring Theory; Recent Advances, Chapter 3, Kluwer Academic Publishers, 2000. Zbl1079.13509MR1858157
2. [2] S. Bazzoni, Class semigroups of Prüfer domains, J. Algebra, 184 (1996), pp. 613–631. Zbl0856.13014MR1409233
3. [3] S. Bazzoni, Groups in the class semigroups of Prüfer domains of finite character, Comm. Algebra, 28 (2000), pp. 5157–5167. Zbl0997.13005MR1785492
4. [4] S. Bazzoni, Clifford regular domains, J. Algebra, 238 (2001), pp. 703–722. Zbl1027.13011MR1823781
5. [5] S. Bazzoni, Finite character of finitely stable domains, J. Pure Appl. Algebra, to appear. Zbl1214.13007MR2769222
6. [6] S. Bazzoni - L. Salce, Groups in the class semigroups of valuation domains, Israel J. Math., 95 (1996), pp. 135–155. Zbl0869.13006MR1418291
7. [7] N. Bourbaki, Algèbre Commutative, Hermann, Paris, 1964. MR194450
8. [8] G. W. Chang - M. Zafrullah, The $w$ -integral closure of integral domains, J. Algebra, 295 (2006), pp. 195–210. Zbl1096.13008MR2188857
9. [9] D. E. Dobbs - E. G. Houston - T. G. Lucas - M. Zafrullah, $t$ -linked overrings and Prüfer $v$ -multiplication domains, Comm. Algebra, 17 (1989), pp. 2835–2852. Zbl0691.13015MR1025612
10. [10] S. El Baghdadi - M. Fontana - G. Picozza, Semistar Dedekind domains, J. Pure Applied Algebra, 193 (2004), pp. 27–60. Zbl1081.13003MR2076377
11. [11] S. El Baghdadi - S. Gabelli, $w$ -divisorial domains, J. Algebra, 285 (2005), pp. 335–355. Zbl1094.13037MR2119116
12. [12] J. Elliot, Functorial properties of star operations, Comm. Algebra, 38 (2010), pp. 1466–1490. Zbl1200.13006MR2656588
13. [13] M. Fontana - K. A. Loper, Kronecker function rings: a general approach, Ideal theoretic methods in commutative algebra (Columbia, MO, 1999), Lecture Notes in Pure and Appl. Math., vol. 220 (Dekker, New York, 2001), pp. 189–205. Zbl1042.13002MR1836601
14. [14] S. Gabelli - E. Houston, Ideal Theory in Pullbacks, Non-Noetherian Commutative Ring Theory; Recent Advances, Chapter 9, Kluwer Academic Publishers, 2000. Zbl1094.13501MR1858163
15. [15] S. Gabelli - G. Picozza, Star-stable domains, J. Pure Applied Algebra, 208 (2007), pp. 853–866. Zbl1174.13004MR2283430
16. [16] S. Gabelli - G. Picozza, Stability and regularity with respect to star operations, Comm. Algebra, to appear. Zbl1260.13004
17. [17] R. Gilmer, Multiplicative ideal theory. Pure and Applied Mathematics, No. 12. Marcel Dekker, Inc., New York, 1972. Zbl0248.13001MR427289
18. [18] F. Halter-Koch, Clifford semigroups of ideals in monoids and domains, Forum Math., 21 (2009), pp. 1001–1020. Zbl1189.13002MR2574145
19. [19] J. R. Hedstrom - E. G. Houston, Pseudo-valuation domains. II. Pacific J. Math., 75, no. 1 (1978), pp. 137–147. Zbl0368.13002MR485811
20. [20] S. Kabbaj - A. Mimouni, Class semigroups of integral domains, J. Algebra, 264 (2003), pp. 620–640. Zbl1027.13012MR1981425
21. [21] S. Kabbaj - A. Mimouni, $t$ -Class semigroups of integral domains, J. reine angew. Math., 612 (2007), pp. 213–229. Zbl1151.13003MR2364057
22. [22] S. Kabbaj - A. Mimouni, Constituent groups of Clifford semigroups arising from $t$ -closure, J. Algebra, 321 (2009), pp. 1443–1452. Zbl1173.13020MR2494399
23. [23] S. Kabbaj - A. Mimouni, $t$ -Class semigroups of Noetherian domains, Commutative Algebra and its applications, de Gruyter (2009), pp. 283–290. Zbl1177.13029MR2606293
24. [24] B. G. Kang, Prüfer $v$ -multiplication domains and the ring $R{\left[X\right]}_{N_v}$ , J. Algebra, 123 (1989), pp. 151-170. Zbl0668.13002MR1000481
25. [25] A. Mimouni, Pullbacks and coherent-like properties, Advances in commutative ring theory (Fez, 1997), pp. 437–459, Lecture Notes in Pure and Appl. Math., 205 (Dekker, New York, 1999). Zbl0963.13005MR1767424
26. [26] B. Olberding, Globalizing local properties of Prüfer domains, J. Algebra, 205, no. 2 (1998), pp. 480–504. Zbl0928.13013MR1632741
27. [27] B. Olberding, Stability, duality and $2$ -generated ideals, and a canonical decomposition of modules, Rend. Sem. Mat. Univ. Padova, 106 (2001), pp. 261–290. Zbl1072.13506MR1876223
28. [28] B. Olberding, On the classification of stable domains, J. Algebra, 243, no. 1 (2001), pp. 177–197. Zbl1042.13013MR1851660
29. [29] B. Olberding, On the structure of stable domains, Comm. Algebra, 30, no. 2 (2002), pp. 877–895. Zbl1073.13014MR1883031
30. [30] B. Olberding, An exceptional class of stable domains, Communication at AMS Meeting $♯$ 991, Special Session on Commutative Rings and Monoids, Chapel Hill, NC, October 2003. 
31. [31] G. Picozza, Star operations on overrings and semistar operations, Comm. Algebra, 33 (2005), pp. 2051–2073. Zbl1088.13001MR2150860
32. [32] D. Rush, Two-generated ideals and representations of abelian groups over valuation rings. J. Algebra, 177, no. 1 (1995), pp. 77–101. Zbl0846.16023MR1356360
33. [33] Wang Fanggui - R. L. McCasland, On strong Mori domains, J. Pure Appl. Algebra, 135 (1999), pp. 155–165. Zbl0943.13017MR1667555
34. [34] P. Zanardo - U. Zannier, The class semigroup of orders in number fields, Math. Proc. Cambridge Philos. Soc., 115 (1994), pp. 379–391. Zbl0828.11068MR1269926

1. Stefania Gabelli, Finite character, local stability property and local invertibility property