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Gr?bner-shirshov Bases

Gr?Bner Shirshov Bases: Normal Forms, Combinatorial And Decision Problems In Algebra


The book is about (associative, Lie and other) algebras, groups, semigroups presented by generators and defining relations. They play a great role in modern mathematics. It is enough to mention the quantum groups and Hopf algebra theory, the Kac Moody and Borcherds algebra theory, the braid groups and Hecke algebra theory, the Coxeter groups and semisimple Lie algebra theory, the plactic monoid theory. One of the main problems for such presentations is the problem of normal forms of their elements. Classical examples of such normal forms give the Poincar Birkhoff Witt theorem for universal enveloping algebras and Artin Markov normal form theorem for braid groups in Burau generators.What is now called Gr bner Shirshov bases theory is a general approach to the problem. It was created by a Russian mathematician A I Shirshov (1921 1981) for Lie algebras (explicitly) and associative algebras (implicitly) in 1962. A few years later, H Hironaka created a theory of standard bases for topological commutative algebra and B Buchberger initiated this kind of theory for commutative algebras, the Gr bner basis theory. The Shirshov paper was largely unknown outside Russia. The book covers this gap in the modern mathematical literature. Now Gr bner Shirshov bases method has many applications both for classical algebraic structures (associative, Lie algebra, groups, semigroups) and new structures (dialgebra, pre-Lie algebra, Rota Baxter algebra, operads). This is a general and powerful method in algebra.



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    • Good (G): Average used book with all pages present. Possible loose bindings, highlighting, cocked spine or torn dust jackets. Used textbooks do not come with supplemental materials.
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    Conditions Guide
  • Format: Hardcover
  • Sold by: --
  • Language: English
  • Publisher: World Scientific Pub Co Inc
  • ISBN-13: 9789814619486
  • ISBN: 9814619485
  • Publication Year: 2019
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HPB condition ratings
  • New: Item is brand new, unused and unmarked, in flawless condition.
  • Fine/Like New (F): No defects, little usage. May show remainder marks. Older books may show minor flaws.
  • Very Good (VG): Shows some signs of wear and is no longer fresh. Attractive. Used textbooks do not come with supplemental materials.
  • Good (G): Average used book with all pages present. Possible loose bindings, highlighting, cocked spine or torn dust jackets. Used textbooks do not come with supplemental materials.
  • Fair (FR): Obviously well-worn, but no text pages missing. May be without endpapers or title page. Markings do not interfere with readability. Used textbooks do not come with supplemental materials.
  • Poor (P): All text is legible but may be soiled and have binding defects. Reading copies and binding copies fall into this category. Used textbooks do not come with supplemental materials.
Conditions Guide
HPB condition ratings
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Conditions Guide
HPB condition ratings
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