Real Nullstellensatz and sums of squares

Michalska, Maria

dc.contributor.author	Michalska, Maria
dc.contributor.editor	Krasiński, Tadeusz
dc.contributor.editor	Spodzieja, Stanisław
dc.date.accessioned	2022-12-22T15:42:36Z
dc.date.available	2022-12-22T15:42:36Z
dc.date.issued	2022
dc.identifier.citation	Michalska M., Real Nullstellensatz and sums of squares, [in:] Analitic and Algebraic Geometry 4, T. Krasiński, S. Spodzieja (ed.), WUŁ, Łódź 2022, https://doi.org/10.18778/8331-092-3.10	pl_PL
dc.identifier.isbn	978-83-8331-092-3
dc.identifier.uri	http://hdl.handle.net/11089/44817
dc.description.abstract	In this paper we highlight the foundational principles of sums of squares in the study of Real Algebraic Geometry. To this aim the article is designed as mainly a self-contained presentation of a variation of the standard proof of Real Nullstellensatz, the only relevant omission being the (long) proof of the Tarski-Seidenberg theorem. On the way we see how the theory follows closely developments in algebra and model theory due to Artin and Schreier. This allows us to present on the way Artin’s solution to Hilbert’s 17th Problem: whether positive polynomials are sums of squares. These notes are intended to be accessible to math students of any level.	pl_PL
dc.language.iso	en	pl_PL
dc.publisher	Wydawnictwo Uniwersytetu Łódzkiego	pl_PL
dc.relation.ispartof	Analitic and Algebraic Geometry 4;
dc.rights	Attribution-NonCommercial-NoDerivatives 4.0 Międzynarodowe	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/	*
dc.subject	Nullstellensatz	pl_PL
dc.subject	Artin-Schreier	pl_PL
dc.subject	Hilbert’s 17th Problem	pl_PL
dc.subject	sums of squares	pl_PL
dc.title	Real Nullstellensatz and sums of squares	pl_PL
dc.type	Book chapter	pl_PL
dc.page.number	121-136	pl_PL
dc.contributor.authorAffiliation	Uniwersytet Łódzki, Wydział Matematyki i Informatyki	pl_PL
dc.identifier.eisbn	978-83-8331-093-0
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dc.contributor.authorEmail	maria.michalska@wmii.uni.lodz.pl	pl_PL
dc.identifier.doi	10.18778/8331-092-3.10