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* Henri Lombardi, Claude Quitté, Commutative algebra: Constructive methods. Finite projective modules, arXiv:1605.04832 [math.AC], May 16 2016, http://arxiv.org/abs/1605.04832, 10.1007/978-94-017-9944-7, http://dx.doi.org/10.1007/978-94-017-9944-7, Series Algebra and Applications, Vol. 20 Translated from the French (Calvage \& Mounet, 2011, revised and extended by the authors) by Tania K. Roblot, Springer, 2015
 
* Henri Lombardi, Claude Quitté, Commutative algebra: Constructive methods. Finite projective modules, arXiv:1605.04832 [math.AC], May 16 2016, http://arxiv.org/abs/1605.04832, 10.1007/978-94-017-9944-7, http://dx.doi.org/10.1007/978-94-017-9944-7, Series Algebra and Applications, Vol. 20 Translated from the French (Calvage \& Mounet, 2011, revised and extended by the authors) by Tania K. Roblot, Springer, 2015
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== 노트 ==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q727659 Q727659]
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===말뭉치===
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# Commutative algebra evolved from problems arising in number theory and algebraic geometry.<ref name="ref_a3cba459">[https://encyclopediaofmath.org/wiki/Commutative_algebra Encyclopedia of Mathematics]</ref>
 +
# In parallel with this, the formation of multi-dimensional commutative algebra was taking place in algebraic geometry.<ref name="ref_a3cba459" />
 +
# The next development of the ideas of commutative algebra is connected with homological methods, the functorial approach and further geometrization.<ref name="ref_a3cba459" />
 +
# This was furthered by the trend, going back to Dedekind and Noether, towards the linearization of commutative algebra, according to which ideals of a ring are regarded as special cases of modules.<ref name="ref_a3cba459" />
 +
# Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.<ref name="ref_cf27ee76">[https://en.wikipedia.org/wiki/Commutative_algebra Commutative algebra]</ref>
 +
# Both algebraic geometry and algebraic number theory build on commutative algebra.<ref name="ref_cf27ee76" />
 +
# Many other notions of commutative algebra are counterparts of geometrical notions occurring in algebraic geometry.<ref name="ref_cf27ee76" />
 +
# To this day, Krull's principal ideal theorem is widely considered the single most important foundational theorem in commutative algebra.<ref name="ref_cf27ee76" />
 +
# Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry.<ref name="ref_685858d1">[https://link.springer.com/book/10.1007/978-1-4612-5350-1 Commutative Algebra]</ref>
 +
# One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it.<ref name="ref_685858d1" />
 +
# This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry.<ref name="ref_685858d1" />
 +
# Commutative algebra is the subject studying commutative algebras.<ref name="ref_b7db0cd3">[https://ncatlab.org/nlab/show/commutative+algebra commutative algebra in nLab]</ref>
 +
# The term "commutative algebra" also refers to the branch of abstract algebra that studies commutative rings.<ref name="ref_e5237dbd">[https://mathworld.wolfram.com/CommutativeAlgebra.html Commutative Algebra -- from Wolfram MathWorld]</ref>
 +
# As a subject on its own, commutative algebra began under the name “ideal theory” with the work of mathematician Richard Dedekind, a giant of the late 19th and early 20th centuries.<ref name="ref_7cd08db7">[https://science.utah.edu/faculty/commutative-algebra/ College of Science]</ref>
 +
# “One of the things I enjoy about my research is how commutative algebra has so many connections to other things,” said Iyengar.<ref name="ref_7cd08db7" />
 +
# In recent years, ideas and techniques from commutative algebra have begun to play an increasingly prominent role in coding theory, in reconstructions, and biology with neural networks.<ref name="ref_7cd08db7" />
 +
# Commutative algebra was born in the 19th century from algebraic geometry, invariant theory, and number theory.<ref name="ref_c104b25b">[https://www.msri.org/programs/267 Mathematical Sciences Research Institute]</ref>
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# On the other hand, you can find all the material covered in any reasonable commutative algebra books.<ref name="ref_0485a803">[https://www.math.columbia.edu/~dejong/courses/commutative_algebra_old/index.html Commutative Algebra]</ref>
 +
# The main purpose of the school is to present both, basic aspects of commutative algebra as well as more advanced tools focused on applications to combinatorics, coding theory and statistics.<ref name="ref_6c3d8e82">[https://www.cimpa.info/en/node/5842 Commutative Algebra with Applications to Statistics and Coding Theory]</ref>
 +
# Shortly thereafter, Bourbaki’s treatise on commutative algebra (Hermann, 1960–1961) was published, but this is an encyclopedic work, good for reference but hardly a textbook for the newcomer.<ref name="ref_def6ce28">[https://www.maa.org/press/maa-reviews/commutative-algebra-i Commutative Algebra I]</ref>
 +
# The Zariski-Samuel books on commutative algebra helped put the subject within reach of anyone interested on it.<ref name="ref_def6ce28" />
 +
# One should also point out that what one usually means by commutative algebra starts properly in chapter 3 of the first volume.<ref name="ref_def6ce28" />
 +
# This course provides an introduction to commutative algebra as a foundation for and first steps towards algebraic geometry.<ref name="ref_f3f902ec">[https://metaphor.ethz.ch/x/2019/hs/401-3132-00L/ Commutative Algebra Autumn 2019]</ref>
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# Commutative algebra is essentially the study of the rings occurring in algebraic number theory and algebraic geometry.<ref name="ref_4c1c5961">[https://www.classcentral.com/course/swayam-commutative-algebra-13008 Free Online Course: Commutative Algebra from Swayam]</ref>
 +
# The main purpose of this course is to provide important workhorses of commutative algebra assuming only basic course on commutative algebra.<ref name="ref_4c1c5961" />
 +
# Apart from deepening the knowledge in commutative algebra, participants of this course are prepared to continue their studies in different directions, for example, algebraic geometry.<ref name="ref_4c1c5961" />
 +
# The material will overlap with a number of references, but the following books cover many of the subjects: M.F. Atiyah and I.G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley 1969.<ref name="ref_05a12e12">[https://www.maths.usyd.edu.au/u/UG/HM/MATH4312/ MATH4312 Commutative Algebra]</ref>
 +
# This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra.<ref name="ref_b013fe54">[https://www.worldscientific.com/worldscibooks/10.1142/7725 Introduction to Algebraic Geometry and Commutative Algebra]</ref>
 +
# Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra.<ref name="ref_b013fe54" />
 +
# Commutative Algebra, the study of commutative rings and their modules, emerged as a definite area of mathematics at the beginning of the twentieth century.<ref name="ref_fb53ddb0">[https://www.math.uconn.edu/~glaz/math5020f14/ MATH 5020: Introduction to Commutative Algebra]</ref>
 +
# Today Commutative Algebra is a deep and beautiful area of study in its own right, which both draws on, and is applicable to, all the disciplines that contributed to its development.<ref name="ref_fb53ddb0" />
 +
# In this course we will study the fundamental notions and methods of research of commutative algebra.<ref name="ref_fb53ddb0" />
 +
 +
===소스===
 +
<references />
 +
 +
== 메타데이터 ==
 +
 +
===위키데이터===
 +
* ID :  [https://www.wikidata.org/wiki/Q727659 Q727659]
 +
===Spacy 패턴 목록===
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* [{'LOWER': 'commutative'}, {'LEMMA': 'algebra'}]

2021년 2월 17일 (수) 03:17 기준 최신판

개요

리뷰, 에세이, 강의노트

  • Henri Lombardi, Claude Quitté, Commutative algebra: Constructive methods. Finite projective modules, arXiv:1605.04832 [math.AC], May 16 2016, http://arxiv.org/abs/1605.04832, 10.1007/978-94-017-9944-7, http://dx.doi.org/10.1007/978-94-017-9944-7, Series Algebra and Applications, Vol. 20 Translated from the French (Calvage \& Mounet, 2011, revised and extended by the authors) by Tania K. Roblot, Springer, 2015

노트

위키데이터

말뭉치

  1. Commutative algebra evolved from problems arising in number theory and algebraic geometry.[1]
  2. In parallel with this, the formation of multi-dimensional commutative algebra was taking place in algebraic geometry.[1]
  3. The next development of the ideas of commutative algebra is connected with homological methods, the functorial approach and further geometrization.[1]
  4. This was furthered by the trend, going back to Dedekind and Noether, towards the linearization of commutative algebra, according to which ideals of a ring are regarded as special cases of modules.[1]
  5. Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.[2]
  6. Both algebraic geometry and algebraic number theory build on commutative algebra.[2]
  7. Many other notions of commutative algebra are counterparts of geometrical notions occurring in algebraic geometry.[2]
  8. To this day, Krull's principal ideal theorem is widely considered the single most important foundational theorem in commutative algebra.[2]
  9. Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry.[3]
  10. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it.[3]
  11. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry.[3]
  12. Commutative algebra is the subject studying commutative algebras.[4]
  13. The term "commutative algebra" also refers to the branch of abstract algebra that studies commutative rings.[5]
  14. As a subject on its own, commutative algebra began under the name “ideal theory” with the work of mathematician Richard Dedekind, a giant of the late 19th and early 20th centuries.[6]
  15. “One of the things I enjoy about my research is how commutative algebra has so many connections to other things,” said Iyengar.[6]
  16. In recent years, ideas and techniques from commutative algebra have begun to play an increasingly prominent role in coding theory, in reconstructions, and biology with neural networks.[6]
  17. Commutative algebra was born in the 19th century from algebraic geometry, invariant theory, and number theory.[7]
  18. On the other hand, you can find all the material covered in any reasonable commutative algebra books.[8]
  19. The main purpose of the school is to present both, basic aspects of commutative algebra as well as more advanced tools focused on applications to combinatorics, coding theory and statistics.[9]
  20. Shortly thereafter, Bourbaki’s treatise on commutative algebra (Hermann, 1960–1961) was published, but this is an encyclopedic work, good for reference but hardly a textbook for the newcomer.[10]
  21. The Zariski-Samuel books on commutative algebra helped put the subject within reach of anyone interested on it.[10]
  22. One should also point out that what one usually means by commutative algebra starts properly in chapter 3 of the first volume.[10]
  23. This course provides an introduction to commutative algebra as a foundation for and first steps towards algebraic geometry.[11]
  24. Commutative algebra is essentially the study of the rings occurring in algebraic number theory and algebraic geometry.[12]
  25. The main purpose of this course is to provide important workhorses of commutative algebra assuming only basic course on commutative algebra.[12]
  26. Apart from deepening the knowledge in commutative algebra, participants of this course are prepared to continue their studies in different directions, for example, algebraic geometry.[12]
  27. The material will overlap with a number of references, but the following books cover many of the subjects: M.F. Atiyah and I.G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley 1969.[13]
  28. This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra.[14]
  29. Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra.[14]
  30. Commutative Algebra, the study of commutative rings and their modules, emerged as a definite area of mathematics at the beginning of the twentieth century.[15]
  31. Today Commutative Algebra is a deep and beautiful area of study in its own right, which both draws on, and is applicable to, all the disciplines that contributed to its development.[15]
  32. In this course we will study the fundamental notions and methods of research of commutative algebra.[15]

소스

  1. ↑ 1.0 1.1 1.2 1.3 Encyclopedia of Mathematics
  2. ↑ 2.0 2.1 2.2 2.3 Commutative algebra
  3. ↑ 3.0 3.1 3.2 Commutative Algebra
  4. ↑ commutative algebra in nLab
  5. ↑ Commutative Algebra -- from Wolfram MathWorld
  6. ↑ 6.0 6.1 6.2 College of Science
  7. ↑ Mathematical Sciences Research Institute
  8. ↑ Commutative Algebra
  9. ↑ Commutative Algebra with Applications to Statistics and Coding Theory
  10. ↑ 10.0 10.1 10.2 Commutative Algebra I
  11. ↑ Commutative Algebra Autumn 2019
  12. ↑ 12.0 12.1 12.2 Free Online Course: Commutative Algebra from Swayam
  13. ↑ MATH4312 Commutative Algebra
  14. ↑ 14.0 14.1 Introduction to Algebraic Geometry and Commutative Algebra
  15. ↑ 15.0 15.1 15.2 MATH 5020: Introduction to Commutative Algebra

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'commutative'}, {'LEMMA': 'algebra'}]
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