LEADER 03938nam  22006615  450 
001 996466377803316
005 20200707010132.0
010   $a3-319-19494-1
024 7 $a10.1007/978-3-319-19494-3
035   $a(CKB)4340000000001627
035   $a(SSID)ssj0001599530
035   $a(PQKBManifestationID)16305990
035   $a(PQKBTitleCode)TC0001599530
035   $a(PQKBWorkID)14892354
035   $a(PQKB)10851625
035   $a(DE-He213)978-3-319-19494-3
035   $a(MiAaPQ)EBC5594352
035   $a(PPN)190373733
035   $a(EXLCZ)994340000000001627
100   $a20151211d2015      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aConstructive Commutative Algebra$b[electronic resource] $eProjective Modules Over Polynomial Rings and Dynamical Gröbner Bases /$fby Ihsen Yengui
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015.
215   $a1 online resource (VII, 271 p. 5 illus.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2138
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-319-19493-3 
327   $aProjective modules over polynomial rings -- Dynamical Gr¨obner bases -- Syzygies in polynomial rings over valuation domains -- Exercises -- Detailed solutions to the exercises.
330   $aThe main goal of this book is to find the constructive content hidden in abstract proofs of concrete theorems in Commutative Algebra, especially in well-known theorems concerning projective modules over polynomial rings (mainly the Quillen-Suslin theorem) and syzygies of multivariate polynomials with coefficients in a valuation ring. Simple and constructive proofs of some results in the theory of projective modules over polynomial rings are also given, and light is cast upon recent progress on the Hermite ring and Gröbner ring conjectures. New conjectures on unimodular completion arising from our constructive approach to the unimodular completion problem are presented. Constructive algebra can be understood as a first preprocessing step for computer algebra that leads to the discovery of general algorithms, even if they are sometimes not efficient. From a logical point of view, the dynamical evaluation gives a constructive substitute for two highly nonconstructive tools of abstract algebra: the Law of Excluded Middle and Zorn's Lemma. For instance, these tools are required in order to construct the complete prime factorization of an ideal in a Dedekind ring, whereas the dynamical method reveals the computational content of this construction. These lecture notes follow this dynamical philosophy.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2138
606   $aCommutative algebra
606   $aCommutative rings
606   $aMathematical logic
606   $aComputer science?Mathematics
606   $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043
606   $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005
606   $aSymbolic and Algebraic Manipulation$3https://scigraph.springernature.com/ontologies/product-market-codes/I17052
615  0$aCommutative algebra.
615  0$aCommutative rings.
615  0$aMathematical logic.
615  0$aComputer science?Mathematics.
615 14$aCommutative Rings and Algebras.
615 24$aMathematical Logic and Foundations.
615 24$aSymbolic and Algebraic Manipulation.
676   $a512.4
700   $aYengui$b Ihsen$4aut$4http://id.loc.gov/vocabulary/relators/aut$0718166
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996466377803316
996   $aConstructive commutative algebra$91392311
997   $aUNISA