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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

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위키데이터

• ID : Q727659

말뭉치

1. Commutative algebra evolved from problems arising in number theory and algebraic geometry.
2. In parallel with this, the formation of multi-dimensional commutative algebra was taking place in algebraic geometry.
3. The next development of the ideas of commutative algebra is connected with homological methods, the functorial approach and further geometrization.
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.
5. Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.
6. Both algebraic geometry and algebraic number theory build on commutative algebra.
7. Many other notions of commutative algebra are counterparts of geometrical notions occurring in algebraic geometry.
8. To this day, Krull's principal ideal theorem is widely considered the single most important foundational theorem in commutative algebra.
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.
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.
11. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry.
12. Commutative algebra is the subject studying commutative algebras.
13. The term "commutative algebra" also refers to the branch of abstract algebra that studies commutative rings.
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.
15. “One of the things I enjoy about my research is how commutative algebra has so many connections to other things,” said Iyengar.
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.
17. Commutative algebra was born in the 19th century from algebraic geometry, invariant theory, and number theory.
18. On the other hand, you can find all the material covered in any reasonable commutative algebra books.
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.
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.
21. The Zariski-Samuel books on commutative algebra helped put the subject within reach of anyone interested on it.
22. One should also point out that what one usually means by commutative algebra starts properly in chapter 3 of the first volume.
23. This course provides an introduction to commutative algebra as a foundation for and first steps towards algebraic geometry.
24. Commutative algebra is essentially the study of the rings occurring in algebraic number theory and algebraic geometry.
25. The main purpose of this course is to provide important workhorses of commutative algebra assuming only basic course on commutative algebra.
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.
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.
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.
29. Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra.
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.
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.
32. In this course we will study the fundamental notions and methods of research of commutative algebra.

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위키데이터

• ID : Q727659

Spacy 패턴 목록

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