Marco Fontana - Academia.edu (original) (raw)
Papers by Marco Fontana
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De Gruyter eBooks, Sep 15, 2009
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arXiv (Cornell University), Jan 13, 2009
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Communications in Algebra, 1996
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Commutative Algebra and its Applications, 2009
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M. Dekker eBooks, 1999
... In addition, DE Dobbs thanks the University of Tennessee, Knoxville, for travel support. We a... more ... In addition, DE Dobbs thanks the University of Tennessee, Knoxville, for travel support. We also thank Maria Allegra, our editor at Marcel Dekker, Inc., for her encouragement and cooperation. David E. Dobbs Marco Font ana Salah-Eddine Kabbaj lii Page 12. Page 13. ...
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Journal of Algebra and Its Applications, Jul 24, 2016
Let [Formula: see text] be an integral domain with quotient field [Formula: see text]. Call an ov... more Let [Formula: see text] be an integral domain with quotient field [Formula: see text]. Call an overring [Formula: see text] of [Formula: see text] a subring of [Formula: see text] containing [Formula: see text] as a subring. A family [Formula: see text] of overrings of [Formula: see text] is called a defining family of [Formula: see text], if [Formula: see text]. Call an overring [Formula: see text] a sublocalization of [Formula: see text], if [Formula: see text] has a defining family consisting of rings of fractions of [Formula: see text]. Sublocalizations and their intersections exhibit interesting examples of semistar or star operations [D. D. Anderson, Star operations induced by overrings, Comm. Algebra 16 (1988) 2535–2553]. We show as a consequence of our work that domains that are locally finite intersections of Prüfer [Formula: see text]-multiplication (respectively, Mori) sublocalizations turn out to be Prüfer [Formula: see text]-multiplication domains (PvMDs) (respectively, Mori); in particular, for the Mori domain case, we reobtain a special case of Théorème 1 of [J. Querré, Intersections d’anneaux intègers, J. Algebra 43 (1976) 55–60] and Proposition 3.2 of [N. Dessagnes, Intersections d’anneaux de Mori — exemples, Port. Math. 44 (1987) 379–392]. We also show that, more than the finite character of the defining family, it is the finite character of the star operation induced by the defining family that causes the interesting results. As a particular case of this theory, we provide a purely algebraic approach for characterizing P vMDs as a subclass of the class of essential domains (see also Theorem 2.4 of [C. A. Finocchiaro and F. Tartarone, On a topological characterization of Prüfer [Formula: see text]-multiplication domains among essential domains, preprint (2014), arXiv:1410.4037]).
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De Gruyter eBooks, Sep 15, 2009
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This volume contains selected refereed papers based on lectures presented at the 'Fifth Inter... more This volume contains selected refereed papers based on lectures presented at the 'Fifth International Fez Conference on Commutative Algebra and Applications' that was held in Fez, Morocco in June 2008. The volume represents new trends and areas of classical research within the field, with contributions from many different countries. In addition, the volume has as a special focus the research and influence of Alain Bouvier on commutative algebra over the past thirty years.
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Communications in Algebra, Nov 11, 2016
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De Gruyter eBooks, Sep 15, 2009
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Springer eBooks, Aug 27, 2010
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Communications in Algebra, Aug 18, 2009
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CRC Press eBooks, Jun 10, 2023
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Journal of Algebra, 2008
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arXiv (Cornell University), May 23, 2006
Special attention is devoted to the ideal-theoretic properties of RJoinER\JoinERJoinE and to the topologica... more Special attention is devoted to the ideal-theoretic properties of RJoinER\JoinERJoinE and to the topological structure of its prime spectrum.
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arXiv (Cornell University), May 7, 2004
Let DDD be an integral domain and star\starstar a semistar operation on DDD. As a generalization of the... more Let DDD be an integral domain and star\starstar a semistar operation on DDD. As a generalization of the notion of Noetherian domains to the semistar setting, we say that DDD is a star\starstar--Noetherian domain if it has the ascending chain condition on the set of its quasi--$\star$--ideals. On the other hand, as an extension the notion of Prüfer domain (and of Prüfer vvv--multiplication domain), we say that DDD is a Prüfer star\starstar--multiplication domain (P$\star$MD, for short) if DMD_MDM is a valuation domain, for each quasi--$\star_{_{f}}$--maximal ideal MMM of DDD. Finally, recalling that a Dedekind domain is a Noetherian Prüfer domain, we define a star\starstar--Dedekind domain to be an integral domain which is star\starstar--Noetherian and a P$\star$MD. In the present paper, after a preliminary study of star\starstar--Noetherian domains, we investigate the star\starstar--Dedekind domains. We extend to the star\starstar--Dedekind domains the main classical results and several characterizations proven for Dedekind domains. In particular, we obtain a characterization of a star\starstar--Dedekind domain by a property of decomposition of any semistar ideal into a ``semistar product'' of prime ideals. Moreover, we show that an integral domain DDD is a star\starstar--Dedekind domain if and only if the Nagata semistar domain Na$(D, \star)$ is a Dedekind domain. Several applications of the general results are given for special cases of the semistar operation star\starstar.
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Commutative Algebra and its Applications, 2009
... we apply this relation with A-1 instead of A and obtain (AvB-l) r-[{A-lrlB-\=(A-lByl-((^-V-1:... more ... we apply this relation with A-1 instead of A and obtain (AvB-l) r-[{A-lrlB-\=(A-lByl-((^-V-1:^-(Av: B) r. Hence Bv is r-invertible by Theorem 3.1 (g), applied with q= v.□ 4 (r,#)-Dedekind and (r,#)-Prufer monoids We use the notions of r-Priifer monids and r-Dedekind monoids (resp. ...
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Journal of Pure and Applied Algebra, Oct 1, 2004
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De Gruyter eBooks, Sep 15, 2009
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arXiv (Cornell University), Jan 13, 2009
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Communications in Algebra, 1996
Bookmarks Related papers MentionsView impact
Commutative Algebra and its Applications, 2009
Bookmarks Related papers MentionsView impact
M. Dekker eBooks, 1999
... In addition, DE Dobbs thanks the University of Tennessee, Knoxville, for travel support. We a... more ... In addition, DE Dobbs thanks the University of Tennessee, Knoxville, for travel support. We also thank Maria Allegra, our editor at Marcel Dekker, Inc., for her encouragement and cooperation. David E. Dobbs Marco Font ana Salah-Eddine Kabbaj lii Page 12. Page 13. ...
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Journal of Algebra and Its Applications, Jul 24, 2016
Let [Formula: see text] be an integral domain with quotient field [Formula: see text]. Call an ov... more Let [Formula: see text] be an integral domain with quotient field [Formula: see text]. Call an overring [Formula: see text] of [Formula: see text] a subring of [Formula: see text] containing [Formula: see text] as a subring. A family [Formula: see text] of overrings of [Formula: see text] is called a defining family of [Formula: see text], if [Formula: see text]. Call an overring [Formula: see text] a sublocalization of [Formula: see text], if [Formula: see text] has a defining family consisting of rings of fractions of [Formula: see text]. Sublocalizations and their intersections exhibit interesting examples of semistar or star operations [D. D. Anderson, Star operations induced by overrings, Comm. Algebra 16 (1988) 2535–2553]. We show as a consequence of our work that domains that are locally finite intersections of Prüfer [Formula: see text]-multiplication (respectively, Mori) sublocalizations turn out to be Prüfer [Formula: see text]-multiplication domains (PvMDs) (respectively, Mori); in particular, for the Mori domain case, we reobtain a special case of Théorème 1 of [J. Querré, Intersections d’anneaux intègers, J. Algebra 43 (1976) 55–60] and Proposition 3.2 of [N. Dessagnes, Intersections d’anneaux de Mori — exemples, Port. Math. 44 (1987) 379–392]. We also show that, more than the finite character of the defining family, it is the finite character of the star operation induced by the defining family that causes the interesting results. As a particular case of this theory, we provide a purely algebraic approach for characterizing P vMDs as a subclass of the class of essential domains (see also Theorem 2.4 of [C. A. Finocchiaro and F. Tartarone, On a topological characterization of Prüfer [Formula: see text]-multiplication domains among essential domains, preprint (2014), arXiv:1410.4037]).
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De Gruyter eBooks, Sep 15, 2009
Bookmarks Related papers MentionsView impact
This volume contains selected refereed papers based on lectures presented at the 'Fifth Inter... more This volume contains selected refereed papers based on lectures presented at the 'Fifth International Fez Conference on Commutative Algebra and Applications' that was held in Fez, Morocco in June 2008. The volume represents new trends and areas of classical research within the field, with contributions from many different countries. In addition, the volume has as a special focus the research and influence of Alain Bouvier on commutative algebra over the past thirty years.
Bookmarks Related papers MentionsView impact
Communications in Algebra, Nov 11, 2016
Bookmarks Related papers MentionsView impact
De Gruyter eBooks, Sep 15, 2009
Bookmarks Related papers MentionsView impact
Springer eBooks, Aug 27, 2010
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Communications in Algebra, Aug 18, 2009
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CRC Press eBooks, Jun 10, 2023
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Journal of Algebra, 2008
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arXiv (Cornell University), May 23, 2006
Special attention is devoted to the ideal-theoretic properties of RJoinER\JoinERJoinE and to the topologica... more Special attention is devoted to the ideal-theoretic properties of RJoinER\JoinERJoinE and to the topological structure of its prime spectrum.
Bookmarks Related papers MentionsView impact
arXiv (Cornell University), May 7, 2004
Let DDD be an integral domain and star\starstar a semistar operation on DDD. As a generalization of the... more Let DDD be an integral domain and star\starstar a semistar operation on DDD. As a generalization of the notion of Noetherian domains to the semistar setting, we say that DDD is a star\starstar--Noetherian domain if it has the ascending chain condition on the set of its quasi--$\star$--ideals. On the other hand, as an extension the notion of Prüfer domain (and of Prüfer vvv--multiplication domain), we say that DDD is a Prüfer star\starstar--multiplication domain (P$\star$MD, for short) if DMD_MDM is a valuation domain, for each quasi--$\star_{_{f}}$--maximal ideal MMM of DDD. Finally, recalling that a Dedekind domain is a Noetherian Prüfer domain, we define a star\starstar--Dedekind domain to be an integral domain which is star\starstar--Noetherian and a P$\star$MD. In the present paper, after a preliminary study of star\starstar--Noetherian domains, we investigate the star\starstar--Dedekind domains. We extend to the star\starstar--Dedekind domains the main classical results and several characterizations proven for Dedekind domains. In particular, we obtain a characterization of a star\starstar--Dedekind domain by a property of decomposition of any semistar ideal into a ``semistar product'' of prime ideals. Moreover, we show that an integral domain DDD is a star\starstar--Dedekind domain if and only if the Nagata semistar domain Na$(D, \star)$ is a Dedekind domain. Several applications of the general results are given for special cases of the semistar operation star\starstar.
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
Commutative Algebra and its Applications, 2009
... we apply this relation with A-1 instead of A and obtain (AvB-l) r-[{A-lrlB-\=(A-lByl-((^-V-1:... more ... we apply this relation with A-1 instead of A and obtain (AvB-l) r-[{A-lrlB-\=(A-lByl-((^-V-1:^-(Av: B) r. Hence Bv is r-invertible by Theorem 3.1 (g), applied with q= v.□ 4 (r,#)-Dedekind and (r,#)-Prufer monoids We use the notions of r-Priifer monids and r-Dedekind monoids (resp. ...
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Journal of Pure and Applied Algebra, Oct 1, 2004
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