| 书目名称 | Constructive Commutative Algebra |
| 副标题 | Projective Modules O |
| 编辑 | Ihsen Yengui |
| 视频video | |
| 概述 | Presents a new point of view concerning problems in Commutative Algebra and Algebraic Geometry.All the proofs are constructive (algorithms) and simple.The reader can easily implement the presented alg |
| 丛书名称 | Lecture Notes in Mathematics |
| 图书封面 |  |
| 描述 | .The 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 toolsof 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 m |
| 出版日期 | Book 2015 |
| 关键词 | 13Cxx,13Pxx,14Qxx,03Fxx; ; Dynamical Gröbner Bases; Dynamical Methods in Commutative Algebra; Gröbner Ri |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-319-19494-3 |
| isbn_softcover | 978-3-319-19493-6 |
| isbn_ebook | 978-3-319-19494-3Series ISSN 0075-8434 Series E-ISSN 1617-9692 |
| issn_series | 0075-8434 |
| copyright | Springer International Publishing Switzerland 2015 |
发表于 2025-3-21 19:11:08
