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Line geometry. --- Geometry, Affine. --- Associative rings.

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This book is a volume of the Springer Briefs in Mathematical Physics and serves as an introductory textbook on the theory of Macdonald polynomials. It is based on a series of online lectures given by the author at the Royal Institute of Technology (KTH), Stockholm, in February and March 2021. Macdonald polynomials are a class of symmetric orthogonal polynomials in many variables. They include important classes of special functions such as Schur functions and Hall–Littlewood polynomials and play important roles in various fields of mathematics and mathematical physics. After an overview of Schur functions, the author introduces Macdonald polynomials (of type A, in the GLn version) as eigenfunctions of a q-difference operator, called the Macdonald–Ruijsenaars operator, in the ring of symmetric polynomials. Starting from this definition, various remarkable properties of Macdonald polynomials are explained, such as orthogonality, evaluation formulas, and self-duality, with emphasis on the roles of commuting q-difference operators. The author also explains how Macdonald polynomials are formulated in the framework of affine Hecke algebras and q-Dunkl operators.

Mathematical physics. --- Special functions. --- Associative rings. --- Associative algebras. --- Mathematical Physics. --- Special Functions. --- Associative Rings and Algebras.

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Rings That are Nearly Associative

Associative rings. --- Rings (Algebra) --- Algebraic rings --- Ring theory --- Algebraic fields

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This beautiful book is the result of the author's wide and deep knowledge of the subject matter, combined with a gift for exposition ... The well selected material is offered in an integrated presentation of the structure theory of noncommutative (associative rings) and its applications. The book will appeal to many a reader. It would be wonderful as a textbook, and in fact, it's based on the author's lecture notes ... Only people looking for the most general form of a particular theorem are advised to turn to other books, but those interested in studying or reviewing its subject matter or looking for a rounded account of it, could do no better than choosing this book for this purpose. Bulletin of the American Mathematical Society Noncommutative Rings provides a cross-section of ideas, techniques and results that give the reader an idea of that part of algebra which concerns itself with noncommutative rings. In the space of 200 pages, Herstein covers the Jacobson radical, semisimple rings, commutativity theorems, simple algebras, representations of finite groups, polynomial identities, Goldie's theorem and the Golod-Shafarevitch theorem. Almost every practicing ring theorist has studied portions of this classic monograph.

Noncommutative rings --- Non-commutative rings --- Associative rings --- Noncommutative rings.

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Ring theory

Rings (Algebra) --- Associative rings. --- Algèbres associatives --- Algèbres non associatives