Picavet, Gabriel; Picavet-L’hermitte, Martine Around Prüfer extensions of rings. (English) Zbl 07800907 Chabert, Jean-Luc (ed.) et al., Algebraic, number theoretic, and topological aspects of ring theory. Selected papers based on the cancelled conference on rings and polynomials, July 2020, and the fourth international meeting on integer-valued polynomials and related topics, CIRM, Luminy, France, July 19–24, 2021. Cham: Springer. 351-382 (2023). MSC: 13B02 13B22 13B40 13B30 PDFBibTeX XMLCite \textit{G. Picavet} and \textit{M. Picavet-L'hermitte}, in: Algebraic, number theoretic, and topological aspects of ring theory. Selected papers based on the cancelled conference on rings and polynomials, July 2020, and the fourth international meeting on integer-valued polynomials and related topics, CIRM, Luminy, France, July 19--24, 2021. Cham: Springer. 351--382 (2023; Zbl 07800907) Full Text: DOI arXiv
Picavet, Gabriel; Picavet-L’Hermitte, Martine Splitting ring extensions. (English) Zbl 1524.13035 Beitr. Algebra Geom. 64, No. 3, 627-668 (2023). Reviewer: Dario Spirito (Padova) MSC: 13B02 13B21 13B22 13B30 13F05 PDFBibTeX XMLCite \textit{G. Picavet} and \textit{M. Picavet-L'Hermitte}, Beitr. Algebra Geom. 64, No. 3, 627--668 (2023; Zbl 1524.13035) Full Text: DOI arXiv
Picavet, Gabriel; Picavet-L’Hermitte, Martine Closures and co-closures attached to FCP ring extensions. (English) Zbl 1518.13008 Palest. J. Math. 11, No. 4, 33-67 (2022). Reviewer: Dario Spirito (Padova) MSC: 13B02 13B22 13B40 PDFBibTeX XMLCite \textit{G. Picavet} and \textit{M. Picavet-L'Hermitte}, Palest. J. Math. 11, No. 4, 33--67 (2022; Zbl 1518.13008) Full Text: arXiv Link
Picavet, Gabriel; Picavet-L’Hermitte, Martine Catenarian FCP ring extensions. (English) Zbl 07556950 J. Commut. Algebra 14, No. 1, 77-93 (2022). MSC: 06D99 13B02 13B21 13B22 12F10 13B30 PDFBibTeX XMLCite \textit{G. Picavet} and \textit{M. Picavet-L'Hermitte}, J. Commut. Algebra 14, No. 1, 77--93 (2022; Zbl 07556950) Full Text: DOI arXiv Link
Picavet, Gabriel; Picavet-L’Hermitte, Martine The Loewy series of an FCP (distributive) ring extension. (English) Zbl 1471.13021 Int. Electron. J. Algebra 29, 15-49 (2021). Reviewer: Owen Biesel (Northfield) MSC: 13B02 13B21 13B22 06E05 06D05 13B30 12F10 PDFBibTeX XMLCite \textit{G. Picavet} and \textit{M. Picavet-L'Hermitte}, Int. Electron. J. Algebra 29, 15--49 (2021; Zbl 1471.13021) Full Text: arXiv Link
Picavet, Gabriel; Picavet-L’Hermitte, Martine FCP \(\Delta\)-extensions of rings. (English) Zbl 1466.13008 Arab. J. Math. 10, No. 1, 211-238 (2021). Reviewer: Grigore Călugăreanu (Cluj-Napoca) MSC: 13B02 13B21 13B22 06E05 06C05 13B30 PDFBibTeX XMLCite \textit{G. Picavet} and \textit{M. Picavet-L'Hermitte}, Arab. J. Math. 10, No. 1, 211--238 (2021; Zbl 1466.13008) Full Text: DOI arXiv
Picavet, Gabriel; Picavet-L’Hermitte, Martine Addendum to: “Modules with finitely many submodules”. (English) Zbl 1467.13012 Int. Electron. J. Algebra 28, 229 (2020). MSC: 13B02 13E10 13B30 13F10 PDFBibTeX XMLCite \textit{G. Picavet} and \textit{M. Picavet-L'Hermitte}, Int. Electron. J. Algebra 28, 229 (2020; Zbl 1467.13012) Full Text: DOI
Picavet, Gabriel; Picavet-L’Hermitte, Martine Boolean FIP ring extensions. (English) Zbl 1439.13023 Commun. Algebra 48, No. 5, 1821-1852 (2020). Reviewer: Grigore Călugăreanu (Cluj-Napoca) MSC: 13B02 13B21 13B22 06E05 06C10 13B30 12F10 06E25 PDFBibTeX XMLCite \textit{G. Picavet} and \textit{M. Picavet-L'Hermitte}, Commun. Algebra 48, No. 5, 1821--1852 (2020; Zbl 1439.13023) Full Text: DOI arXiv
Picavet, Gabriel; Picavet-L’Hermitte, Martine Ring extensions of length two. (English) Zbl 1423.13059 J. Algebra Appl. 18, No. 9, Article ID 1950174, 34 p. (2019). Reviewer: Nikolay I. Kryuchkov (Ryazan) MSC: 13B02 13B21 13B22 13B30 13G05 13B10 PDFBibTeX XMLCite \textit{G. Picavet} and \textit{M. Picavet-L'Hermitte}, J. Algebra Appl. 18, No. 9, Article ID 1950174, 34 p. (2019; Zbl 1423.13059) Full Text: DOI arXiv
Dobbs, David E.; Picavet, Gabriel; Picavet-L’Hermitte, Martine On the number of intermediate rings when a decomposed extension lies atop a ramified extension. II. (English) Zbl 1412.13012 Palest. J. Math. 8, No. 2, 1-7 (2019). MSC: 13B21 13G05 PDFBibTeX XMLCite \textit{D. E. Dobbs} et al., Palest. J. Math. 8, No. 2, 1--7 (2019; Zbl 1412.13012) Full Text: Link
Cahen, Paul-Jean; Picavet, Gabriel; Picavet-L’Hermitte, Martine Pointwise minimal extensions. (English) Zbl 1402.13009 Arab. J. Math. 7, No. 4, 249-271 (2018). Reviewer: Nikolay I. Kryuchkov (Ryazan) MSC: 13B02 13B21 13B22 13B30 PDFBibTeX XMLCite \textit{P.-J. Cahen} et al., Arab. J. Math. 7, No. 4, 249--271 (2018; Zbl 1402.13009) Full Text: DOI
Dobbs, David E.; Picavet, Gabriel; Picavet-L’Hermitte, Martine On the number of intermediate rings when a decomposed extension lies atop a ramified extension. (English) Zbl 1393.13018 Palest. J. Math. 7, No. 2, 363-384 (2018). MSC: 13B21 13G05 PDFBibTeX XMLCite \textit{D. E. Dobbs} et al., Palest. J. Math. 7, No. 2, 363--384 (2018; Zbl 1393.13018) Full Text: Link
Picavet, Gabriel; Picavet-L’Hermitte, Martine Quasi-Prüfer extensions of rings. (English) Zbl 1400.13012 Fontana, Marco (ed.) et al., Rings, polynomials, and modules. Proceedings of the conferences “Recent advances in commutative ring and module theory”, Bressanone/Brixen, Italy, June 13–17, 2016 and “Conference on rings and polynomials”, Graz, Austria, July 3–8, 2016. Cham: Springer (ISBN 978-3-319-65872-8/hbk; 978-3-319-65874-2/ebook). 307-336 (2017). Reviewer: Marco Fontana (Roma) MSC: 13B02 13B22 13A18 13F05 14A05 PDFBibTeX XMLCite \textit{G. Picavet} and \textit{M. Picavet-L'Hermitte}, in: Rings, polynomials, and modules. Proceedings of the conferences ``Recent advances in commutative ring and module theory'', Bressanone/Brixen, Italy, June 13--17, 2016 and ``Conference on rings and polynomials'', Graz, Austria, July 3--8, 2016. Cham: Springer. 307--336 (2017; Zbl 1400.13012) Full Text: DOI arXiv
Picavet, Gabriel; Picavet-L’Hermitte, Martine Étale extensions with finitely many subextensions. (English) Zbl 1393.13017 Boll. Unione Mat. Ital. 10, No. 4, 549-573 (2017). Reviewer: Shreedevi K. Masuti (Genova) MSC: 13B02 13B21 13B22 13E10 13B30 13B40 05A18 13F10 PDFBibTeX XMLCite \textit{G. Picavet} and \textit{M. Picavet-L'Hermitte}, Boll. Unione Mat. Ital. 10, No. 4, 549--573 (2017; Zbl 1393.13017) Full Text: DOI arXiv
Picavet, Gabriel; Picavet-L’Hermitte, Martine Pointwise minimal extensions. arXiv:1708.07983 Preprint, arXiv:1708.07983 [math.AC] (2017). MSC: 13B02 BibTeX Cite \textit{G. Picavet} and \textit{M. Picavet-L'Hermitte}, ``Pointwise minimal extensions'', Preprint, arXiv:1708.07983 [math.AC] (2017) Full Text: arXiv OA License
Picavet, Gabriel; Picavet-L’Hermitte, Martine FIP and FCP products of ring morphisms. (English) Zbl 1346.13013 Palest. J. Math. 5, Spec. Iss., 63-80 (2016). MSC: 13B02 13B21 13B22 13E10 13B30 05A18 13F10 PDFBibTeX XMLCite \textit{G. Picavet} and \textit{M. Picavet-L'Hermitte}, Palest. J. Math. 5, 63--80 (2016; Zbl 1346.13013) Full Text: arXiv Link
Picavet, Gabriel; Picavet-L’Hermitte, Martine Some more combinatorics results on Nagata extensions. (English) Zbl 1346.13012 Palest. J. Math. 5, Spec. Iss., 49-62 (2016). MSC: 13B02 13B21 13B25 12F05 13B22 13B30 PDFBibTeX XMLCite \textit{G. Picavet} and \textit{M. Picavet-L'Hermitte}, Palest. J. Math. 5, 49--62 (2016; Zbl 1346.13012) Full Text: Link
Picavet, Gabriel; Picavet-L’Hermitte, Martine Modules with finitely many submodules. (English) Zbl 1331.13006 Int. Electron. J. Algebra 19, 119-131 (2016); addendum ibid. 28, 229 (2020). Reviewer: Francois Couchot (Caen) MSC: 13B02 13E10 13B30 13F10 PDFBibTeX XMLCite \textit{G. Picavet} and \textit{M. Picavet-L'Hermitte}, Int. Electron. J. Algebra 19, 119--131 (2016; Zbl 1331.13006) Full Text: DOI Link
Dobbs, David E.; Picavet, Gabriel; Picavet-L’Hermitte, Martine Transfer results for the FIP and FCP properties of ring extensions. (English) Zbl 1317.13016 Commun. Algebra 43, No. 3, 1279-1316 (2015). Reviewer: Christodor-Paul Ionescu (Bucureşti) MSC: 13B02 13B21 13B25 PDFBibTeX XMLCite \textit{D. E. Dobbs} et al., Commun. Algebra 43, No. 3, 1279--1316 (2015; Zbl 1317.13016) Full Text: DOI
Picavet, Gabriel; Picavet-L’Hermitte, Martine Prüfer and Morita hulls of FCP extensions. (English) Zbl 1365.13012 Commun. Algebra 43, No. 1, 102-119 (2015). Reviewer: Vivek Sadhu (Mumbai) MSC: 13B02 13B21 13B22 13B30 13B40 PDFBibTeX XMLCite \textit{G. Picavet} and \textit{M. Picavet-L'Hermitte}, Commun. Algebra 43, No. 1, 102--119 (2015; Zbl 1365.13012) Full Text: DOI arXiv
Dobbs, David E.; Picavet, Gabriel; Picavet-L’Hermitte, Martine When an extension of Nagata rings has only finitely many intermediate rings, each of those is a Nagata ring. (English) Zbl 1486.13016 Int. J. Math. Math. Sci. 2014, Article ID 315919, 13 p. (2014). MSC: 13B02 13B21 13G05 13B10 PDFBibTeX XMLCite \textit{D. E. Dobbs} et al., Int. J. Math. Math. Sci. 2014, Article ID 315919, 13 p. (2014; Zbl 1486.13016) Full Text: DOI
Dobbs, David E.; Picavet, Gabriel; Picavet-L’Hermitte, Martine Characterizing the ring extensions that satisfy FIP or FCP. (English) Zbl 1271.13022 J. Algebra 371, 391-429 (2012). Reviewer: Marco Fontana (Roma) MSC: 13B99 13B22 13B21 13A15 13G05 PDFBibTeX XMLCite \textit{D. E. Dobbs} et al., J. Algebra 371, 391--429 (2012; Zbl 1271.13022) Full Text: DOI
Dobbs, David E.; Picavet, Gabriel; Picavet-L’Hermitte, Martine; Shapiro, Jay On intersections and composites of minimal ring extensions. (English) Zbl 1267.13016 JP J. Algebra Number Theory Appl. 26, No. 2, 103-158 (2012). MSC: 13B99 13A15 13B21 12F99 13G05 PDFBibTeX XMLCite \textit{D. E. Dobbs} et al., JP J. Algebra Number Theory Appl. 26, No. 2, 103--158 (2012; Zbl 1267.13016) Full Text: Link
Dobbs, David E.; Picavet, Gabriel; Picavet-L’Hermitte, Martine On finite maximal chains of weak Baer going-down rings. (English) Zbl 1248.13013 Commun. Algebra 40, No. 5, 1843-1855 (2012). Reviewer: Peter Schenzel (Halle) MSC: 13B21 13B99 13A15 13G05 13F05 PDFBibTeX XMLCite \textit{D. E. Dobbs} et al., Commun. Algebra 40, No. 5, 1843--1855 (2012; Zbl 1248.13013) Full Text: DOI
Dobbs, David E.; Picavet, Gabriel On almost-divided domains. (English) Zbl 1187.13020 Rend. Circ. Mat. Palermo (2) 58, No. 2, 199-210 (2009). MSC: 13G05 13A15 13C15 13B30 13F05 PDFBibTeX XMLCite \textit{D. E. Dobbs} and \textit{G. Picavet}, Rend. Circ. Mat. Palermo (2) 58, No. 2, 199--210 (2009; Zbl 1187.13020) Full Text: DOI
Dobbs, David E.; Picavet, Gabriel; Picavet-L’Hermitte, Martine On the maximal cardinality of chains of intermediate rings. (English) Zbl 1161.13302 Int. Electron. J. Algebra 5, 121-134 (2009). MSC: 13B02 13A15 13G05 PDFBibTeX XMLCite \textit{D. E. Dobbs} et al., Int. Electron. J. Algebra 5, 121--134 (2009; Zbl 1161.13302)
Dobbs, David E.; Picavet, Gabriel Straight rings. (English) Zbl 1159.13012 Commun. Algebra 37, No. 3, 757-793 (2009). MSC: 13G05 13B24 13B99 13C99 13F45 13A15 13F05 13E10 PDFBibTeX XMLCite \textit{D. E. Dobbs} and \textit{G. Picavet}, Commun. Algebra 37, No. 3, 757--793 (2009; Zbl 1159.13012) Full Text: DOI
Dobbs, David E.; Picavet, Gabriel; Picavet-L’Hermitte, Martine A characterization of the commutative unital rings with only finitely many unital subrings. (English) Zbl 1173.13008 J. Algebra Appl. 7, No. 5, 601-622 (2008). Reviewer: David F. Anderson (Knoxville) MSC: 13B99 13B21 13G05 13B30 13M99 PDFBibTeX XMLCite \textit{D. E. Dobbs} et al., J. Algebra Appl. 7, No. 5, 601--622 (2008; Zbl 1173.13008) Full Text: DOI
Dobbs, David E.; Mullins, Bernadette; Picavet, Gabriel; Picavet-L’Hermitte, Martine On the FIP property for extensions of commutative rings. (English) Zbl 1120.13009 Commun. Algebra 33, No. 9, 3091-3119 (2005). Reviewer: D. E. Rush (Riverside) MSC: 13B02 13B21 12F05 13E10 13F20 PDFBibTeX XMLCite \textit{D. E. Dobbs} et al., Commun. Algebra 33, No. 9, 3091--3119 (2005; Zbl 1120.13009) Full Text: DOI
Bouacida, Ezzeddine; Echi, Othman; Picavet, Gabriel; Salhi, Ezzeddine An extension theorem for sober spaces and the Goldman topology. (English) Zbl 1042.54003 Int. J. Math. Math. Sci. 2003, No. 51, 3217-3239 (2003). Reviewer: Bernhard Behrens (Göteborg) MSC: 54A10 54B35 54F65 57R30 PDFBibTeX XMLCite \textit{E. Bouacida} et al., Int. J. Math. Math. Sci. 2003, No. 51, 3217--3239 (2003; Zbl 1042.54003) Full Text: DOI EuDML
Picavet, Gabriel Universally going-down rings, 1-split rings, and absolute integral closure. (English) Zbl 1082.13502 Commun. Algebra 31, No. 10, 4655-4685 (2003). MSC: 13B22 13B24 13B02 PDFBibTeX XMLCite \textit{G. Picavet}, Commun. Algebra 31, No. 10, 4655--4685 (2003; Zbl 1082.13502) Full Text: DOI
Picavet, Gabriel About composite rings. (English) Zbl 0901.13017 Cahen, Paul-Jean (ed.) et al., Commutative ring theory. Proceedings of the 2nd international conference, Fès, Morocco, June 5–10, 1995. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 185, 417-442 (1997). Reviewer: Christodor Ionescu (Bucureşti) MSC: 13F20 13B02 13F45 13E05 13C14 PDFBibTeX XMLCite \textit{G. Picavet}, Lect. Notes Pure Appl. Math. 185, 417--442 (1997; Zbl 0901.13017)
Picavet, Gabriel; L’Hermitte-Picavet, Martine \(t\)-closed morphisms. (Morphismes \(t\)-clos.) (French) Zbl 0774.13002 Commun. Algebra 21, No. 1, 179-219 (1993). Reviewer: P.Schenzel (Halle) MSC: 13B10 13B02 14E22 PDFBibTeX XMLCite \textit{G. Picavet} and \textit{M. L'Hermitte-Picavet}, Commun. Algebra 21, No. 1, 179--219 (1993; Zbl 0774.13002) Full Text: DOI
Picavet, Gabriel Pureté, rigidité, et morphismes entiers. (Purity, rigidity, and integral morphisms). (French) Zbl 0747.13006 Trans. Am. Math. Soc. 323, No. 1, 283-313 (1991). Reviewer: Dorin-Mihail Popescu (Vechta) MSC: 13B10 13B02 PDFBibTeX XMLCite \textit{G. Picavet}, Trans. Am. Math. Soc. 323, No. 1, 283--313 (1991; Zbl 0747.13006) Full Text: DOI
Picavet, Gabriel Révêtements étales. (Étale coverings). (French) Zbl 0651.13003 Fundam. Math. 128, 61-65 (1987). Reviewer: R.Y.Sharp MSC: 13B99 14B25 13B02 13E99 PDFBibTeX XMLCite \textit{G. Picavet}, Fundam. Math. 128, 61--65 (1987; Zbl 0651.13003) Full Text: DOI EuDML
Picavet, Gabriel Propriétés et applications de la notion de contenu. (French) Zbl 0584.13004 Commun. Algebra 13, 2231-2265 (1985). Reviewer: D. E. Rush MSC: 13A15 13B02 14A05 PDFBibTeX XMLCite \textit{G. Picavet}, Commun. Algebra 13, 2231--2265 (1985; Zbl 0584.13004) Full Text: DOI