000 | 03706nam a22005535i 4500 | ||
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001 | 978-3-319-19494-3 | ||
003 | DE-He213 | ||
005 | 20210120150115.0 | ||
007 | cr nn 008mamaa | ||
008 | 151211s2015 gw | s |||| 0|eng d | ||
020 |
_a9783319194943 _9978-3-319-19494-3 |
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024 | 7 |
_a10.1007/978-3-319-19494-3 _2doi |
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072 | 7 |
_aPBF _2bicssc |
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_aMAT002010 _2bisacsh |
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_a512.44 _223 |
100 | 1 |
_aYengui, Ihsen. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aConstructive Commutative Algebra _h[electronic resource] : _bProjective Modules Over Polynomial Rings and Dynamical Gröbner Bases / _cby Ihsen Yengui. |
250 | _a1st ed. 2015. | ||
264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2015. |
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300 |
_aVII, 271 p. 5 illus. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2138 |
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505 | 0 | _aProjective modules over polynomial rings -- Dynamical Gr ̈obner bases -- Syzygies in polynomial rings over valuation domains -- Exercises -- Detailed solutions to the exercises. | |
520 | _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. | ||
650 | 0 | _aCommutative algebra. | |
650 | 0 | _aCommutative rings. | |
650 | 0 | _aMathematical logic. | |
650 | 0 | _aComputer science—Mathematics. | |
650 | 1 | 4 |
_aCommutative Rings and Algebras. _0https://scigraph.springernature.com/ontologies/product-market-codes/M11043 |
650 | 2 | 4 |
_aMathematical Logic and Foundations. _0https://scigraph.springernature.com/ontologies/product-market-codes/M24005 |
650 | 2 | 4 |
_aSymbolic and Algebraic Manipulation. _0https://scigraph.springernature.com/ontologies/product-market-codes/I17052 |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer Nature eBook | |
776 | 0 | 8 |
_iPrinted edition: _z9783319194950 |
776 | 0 | 8 |
_iPrinted edition: _z9783319194936 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2138 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-319-19494-3 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-SXMS | ||
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