Necessary conditions for irreducibility of algebroid plane curves

Brzostowski, Szymon

dc.contributor.author	Brzostowski, Szymon
dc.contributor.editor	Krasiński, Tadeusz
dc.contributor.editor	Spodzieja, Stanisław
dc.date.accessioned	2017-12-13T09:47:13Z
dc.date.available	2017-12-13T09:47:13Z
dc.date.issued	2013
dc.identifier.citation	Brzostowski Sz., Necessary conditions for irreducibility of algebroid plane curves, [in:] Krasiński T., Spodzieja S. (eds.), Analytic and Algebraic Geometry, Wydawnictwo Uniwersytetu Łódzkiego, Łódź 2013, s. 33-40, doi: 10.18778/7969-017-6.03	pl_PL
dc.identifier.isbn	978-83-7969-017-6
dc.identifier.uri	http://hdl.handle.net/11089/23606
dc.description.abstract	Let K be an algebraically closed field of characteristic 0 and let ƒ ϵ K[[X]] [Y] be monic. Using the properties of approximate roots given in [J. Algebra 343 (2011), pp. 143-159] we propose some necessary conditions for irreducibility of ƒ in K[[X]] [Y]. The result is expressed only in terms of intersection multiplicities of ƒ with its approximate roots.	pl_PL
dc.language.iso	en	pl_PL
dc.publisher	Wydawnictwo Uniwersytetu Łódzkiego	pl_PL
dc.relation.ispartof	Krasiński T., Spodzieja S. (eds.), Analytic and Algebraic Geometry, Wydawnictwo Uniwersytetu Łódzkiego, Łódź 2013;
dc.rights	Uznanie autorstwa-Użycie niekomercyjne-Bez utworów zależnych 3.0 Polska	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/pl/	*
dc.title	Necessary conditions for irreducibility of algebroid plane curves	pl_PL
dc.type	Book chapter	pl_PL
dc.rights.holder	© Copyright by University of Łódź, Łódź 2013	pl_PL
dc.page.number	33-40	pl_PL
dc.contributor.authorAffiliation	Faculty of Mathematics and Computer Science, University of Lódź ul. Banacha 22, 90-238 Łódź	pl_PL
dc.references	Shreeram Shankar Abhyankar. "Lectures on expansion techniques in algebraic geometry", volume 57 of "Tata Institute of Fundamental Research Lectures on Mathematics and Physics". Tata Institute of Fundamental Research, Bombay (1977). Notes by Balwant Singh.	pl_PL
dc.references	Shreeram Shankar Abhyankar. Irreducibility criterion for germs of analytic functions of two complex variables. Adv. Math. 74(2), 190{257 (1989).	pl_PL
dc.references	Shreeram Shankar Abhyankar. "Algebraic geometry for scientists and engineers", volume 35 of "Mathematical Surveys and Monographs". American Mathematical Society, Providence, RI (1990).	pl_PL
dc.references	Shreeram Shankar Abhyankar and Tzuong Tsieng Moh. Newton-Puiseux expansion and generalized Tschirnhausen transformation. I, II. J. Reine Angew. Math. 260, 47-83 (1973); ibid. 261, 29-54 (1973).	pl_PL
dc.references	Szymon Brzostowski. "Pierwiastki aproksymatywne wielomianów". PhD thesis, Faculty of Mathematics and Computer Science, University of Łódź (2008). (In Polish).	pl_PL
dc.references	Szymon Brzostowski. Non-characteristic approximate roots of polynomials. J. Algebra 343, 143-159 (2011).	pl_PL
dc.references	Antonio Campillo. "Algebroid curves in positive characteristic", volume 813 of "Lecture Notes in Mathematics". Springer, Berlin (1980).	pl_PL
dc.references	Evelia Rosa Garcia Barroso and Janusz Gwoździewicz. Characterization of Jacobian Newton polygons of plane branches and new criteria of irreducibility. Ann. Inst. Fourier (Grenoble) 60(2), 683-709 (2010).	pl_PL
dc.references	Evelia Rosa Garcia Barroso and Arkadiusz Płoski. Euclidean algorithm and polynomial equations after Labatie. (2013). This volume.	pl_PL
dc.references	Arkadiusz Płoski. Introduction to the local theory of plane algebraic curves. (2013). This volume.	pl_PL
dc.contributor.authorEmail	brzosts@math.uni.lodz.pl	pl_PL
dc.identifier.doi	10.18778/7969-017-6.03