Show simple item record

dc.contributor.authorBrzostowski, Szymon
dc.contributor.authorRodak, Tomasz
dc.contributor.editorKrasiński, Tadeusz
dc.contributor.editorSpodzieja, Stanisław
dc.identifier.citationBrzostowski S., Rodak T., The Łojasiewicz exponent via the valuative Hamburger-Noether process, [in:] Krasiński T., Spodzieja S. (eds), Analytic and Algebraic Geometry 2, Łódź University Press, Łódź 2017, p. 51-65, doi: 10.18778/8088-922-4.10pl_PL
dc.description.abstractLet k be an algebraically closed field of any characteristic. We apply the Hamburger-Noether process of successive quadratic transformations to show the equivalence of two definitions of the Łojasiewicz exponent £ (a) of an ideal a ⊂ k[[x; y]].pl_PL
dc.publisherŁódź University Presspl_PL
dc.relation.ispartofKrasiński T., Spodzieja S. (eds), Analytic and Algebraic Geometry 2, Łódź University Press, Łódź 2017;
dc.rightsUznanie autorstwa-Użycie niekomercyjne-Bez utworów zależnych 3.0 Polska*
dc.titleThe Łojasiewicz exponent via the valuative Hamburger-Noether processpl_PL
dc.typeBook chapterpl_PL
dc.rights.holder© Copyright by Authors, Łódź 2017; © Copyright for this edition by Uniwersytet Łódzki, Łódź 2017pl_PL
dc.contributor.authorAffiliationFaculty of Mathematics and Computer Science, University of Łódź, ul. S. Banacha 22, 90-238 Łódź, Polandpl_PL
dc.referencesS. Abhyankar, On the valuations centered in a local domain, Amer. J. Math., 78 (1956), 321–348.pl_PL
dc.referencesN. Bourbaki, Elements of mathematics. Commutative algebra, Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass., 1972. Translated from the French.pl_PL
dc.referencesS. Brzostowski and T. Rodak, The Łojasiewicz exponent over a field of arbitrary characteristic, Rev. Mat. Complut., 28 (2) (2015), 487–504.pl_PL
dc.referencesA. Campillo, Algebroid curves in positive characteristic, Lecture Notes in Mathematics 813, Springer, Berlin, 1980.pl_PL
dc.referencesJ. Chądzyński and T. Krasiński, The Łojasiewicz exponent of an analytic mapping of two complex variables at an isolated zero, in: Singularities (Warsaw, 1985), Banach Center Publ. 20, PWN, Warsaw, 1988, 139–146.pl_PL
dc.referencesJ.O. D’Angelo, Real hypersurfaces, orders of contact, and applications, Annals of Mathematics, 115 (3) (1982), 615–637.pl_PL
dc.referencesA.B. de Felipe, E.R. García Barroso, J. Gwoździewicz and A. Płoski, Łojasiewicz exponents and Farey sequences, Rev. Mat. Complut., 29 (3) (2016), 719–724.pl_PL
dc.referencesC. Galindo, Intersections of 1-forms and valuations in a local regular surface, J. Pure Appl. Algebra, 94 (3) (1994), 307–325.pl_PL
dc.referencesC. Huneke and I. Swanson, Integral closure of ideals, rings, and modules, London Mathematical Society Lecture Note Series 336, Cambridge University Press, Cambridge, 2006.pl_PL
dc.referencesM. Lejeune-Jalabert and B. Teissier, Clôture intégrale des idéaux et équisingularité, Ann. Fac. Sci. Toulouse Math. (6) 17 (2008), no. 4, 781–859.pl_PL
dc.referencesH. Matsumura, Commutative ring theory, Cambridge Studies in Advanced Mathematics, 8, Cambridge University Press, Cambridge, second edition, 1989. Translated from the Japanese by M. Reid.pl_PL
dc.referencesJ.D. McNeal and A. Némethi, The order of contact of a holomorphic ideal in C2, Math. Z. 250 (4) (2005), 873–883.pl_PL
dc.referencesA. Płoski, Introduction to the local theory of plane algebraic curves, in: Analytic and algebraic geometry (Łódz 2013, Faculty of Mathematics and Computer Science. University of Łódź, Łódź, 2013, 115–134.pl_PL
dc.referencesR.J. Walker. Algebraic curves. Dover Publications, Inc., New York, 1962.pl_PL

Files in this item


This item appears in the following Collection(s)

Show simple item record

Uznanie autorstwa-Użycie niekomercyjne-Bez utworów zależnych 3.0 Polska
Except where otherwise noted, this item's license is described as Uznanie autorstwa-Użycie niekomercyjne-Bez utworów zależnych 3.0 Polska