Finite character, local stability property and local invertibility property
Actes des rencontres du CIRM, Tome 2 (2010) no. 2, pp. 119-122.

We illustrate some results relating the finite character property, the local stability property and the local invertibility property of a domain and give a partial answer to two open questions.

Publié le :
DOI : 10.5802/acirm.47
Mots clés : Finite character, stability, Clifford regularity
Gabelli, Stefania 1

1 Dipartimento di Matematica, Università degli Studi Roma Tre, Largo S. L. Murialdo, 1, 00146 Roma, Italy
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Gabelli, Stefania. Finite character, local stability property and local invertibility property. Actes des rencontres du CIRM, Tome 2 (2010) no. 2, pp. 119-122. doi : 10.5802/acirm.47. http://www.numdam.org/articles/10.5802/acirm.47/

[1] S. Bazzoni, Class semigroups of Prüfer domains, J. Algebra 184 (1996), 613–631. | DOI | Zbl

[2] S. Bazzoni, Groups in the class semigroups of Prüfer domains of finite character, Comm. Algebra 28 (2000), 5157–5167. | DOI | Zbl

[3] S. Bazzoni, Clifford regular domains, J. Algebra 238 (2001), 703–722. | DOI | MR | Zbl

[4] S. Bazzoni, Finite character of finitely stable domains, J. Pure Appl. Algebra 215 (2011), 1127–1132. | DOI | MR | Zbl

[5] S. Bazzoni and L. Salce, Groups in the class semigroups of valuation domains, Israel J. Math. 95 (1996), 135–155. | DOI | MR | Zbl

[6] T. Dumitrescu and M. Zafrullah, Characterizing domains of finite *-character, J. Pure Appl. Algebra 214 (2010), 2087–2091 | DOI | Zbl

[7] C.A. Finocchiaro, G. Picozza and F. Tartarone Star-Invertibility and t-finite character in Integral Domains, J. Algebra Appl., to appear. | DOI | MR | Zbl

[8] S. Gabelli and G. Picozza, Star-stable domains, J. Pure Appl. Algebra 208 (2007), 853–866. | DOI | MR | Zbl

[9] S. Gabelli and G. Picozza Stability and regularity with respect to star operations, Comm. Algebra, to appear. | DOI | MR | Zbl

[10] S. Gabelli and G. Picozza, Star stability and star regularity for Mori domains, Rend. Semin. Mat. Univ. Padova, to appear. | DOI | Numdam | MR | Zbl

[11] W.C. Holland, J. Martinez, W.Wm. McGovern and M.Tesemma, Bazzoni’s Conjecture, J. Algebra 320 (2008), 1764–1768. | DOI | MR

[12] W. Wm. McGovern, Prüfer domains with Clifford Class semigroup, J. Comm. Alg., to appear. | DOI | Zbl

[13] B. Olberding, Globalizing local properties of Prüfer domains, J. Algebra 205 (1998), 480–504. | DOI | Zbl

[14] B. Olberding, Stability, duality and 2-generated ideals, and a canonical decomposition of modules, Rend. Semin. Mat. Univ. Padova 106 (2001), 261–290. | Numdam | Zbl

[15] B. Olberding, On the classification of stable domains, J. Algebra 243 (2001), 177–197. | DOI | MR | Zbl

[16] B. Olberding, On the structure of stable domains, Comm. Algebra 30 (2002), 877–895. | DOI | MR | Zbl

[17] D. Rush, Two-generated ideals and representations of abelian groups over valuation rings, J. Algebra 177 (1995), 77–101. | DOI | MR | Zbl

[18] M. Zafrullah, t-Invertibility and Bazzoni-like statements, J. Pure Appl. Algebra 214 (2010), 654–657. | DOI | Zbl

[19] P. Zanardo, The class semigroup of local one-dimensional domains, J. Pure Appl. Algebra 212 (2008), 2259–2270. | DOI | MR | Zbl

[20] P. Zanardo and U. Zannier, The class semigroup of orders in number fields, Math. Proc. Cambridge Philos. Soc. 115 (1994), 379–391. | DOI | MR | Zbl

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