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Titlebook: Algebra II; Textbook for Student Alexey L. Gorodentsev Textbook 2017 Springer International Publishing AG 2017 Fields.Rings.Modules.Groups.

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发表于 2025-3-21 16:22:13 | 显示全部楼层 |阅读模式
期刊全称Algebra II
期刊简称Textbook for Student
影响因子2023Alexey L. Gorodentsev
视频video
发行地址Challenging amount of material thoughtfully organized for deep and fast learning.Large collection of exercises equipped with hints and a lot of problems for independent solution.Simple modern explanat
图书封面Titlebook: Algebra II; Textbook for Student Alexey L. Gorodentsev Textbook 2017 Springer International Publishing AG 2017 Fields.Rings.Modules.Groups.
影响因子.This book is the second volume of an intensive “Russian-style” two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them. .The course covers substantial areas of advanced combinatorics, geometry, linear and multilinear algebra, representation theory, category theory, commutative algebra, Galois theory, and algebraic geometry – topics that are often overlooked in standard undergraduate courses..This textbook is based on courses the author has conducted at the Independent University of Moscow and at the Faculty of Mathematics in the Higher School of Economics. The main content is complemented by a wealth of exercises for class discussion, some of which include comments and hints, as well as problems for independent study..
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发表于 2025-3-21 20:55:18 | 显示全部楼层
https://doi.org/10.1007/978-3-8350-9279-2at (. ∘.) ∘. = . ∘ (. ∘.) for all composable pairs ., . and ., .. Finally, for every ., there exists an . . such that . ∘ Id. = . and Id. ∘. = . for all morphisms .: . → ., .: . → . in .. It is actually unique for every ., because Id.. = Id..∘ Id.. = Id.. for every two such endomorphisms ..
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Categories and Functors,at (. ∘.) ∘. = . ∘ (. ∘.) for all composable pairs ., . and ., .. Finally, for every ., there exists an . . such that . ∘ Id. = . and Id. ∘. = . for all morphisms .: . → ., .: . → . in .. It is actually unique for every ., because Id.. = Id..∘ Id.. = Id.. for every two such endomorphisms ..
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https://doi.org/10.1007/978-3-8350-9279-2Given a set . and a field ., let us write . for the vector space with basis . over .. It is formed by the formal linear combinations .. ⋅ . of elements . ∈ . with coefficients ., all but a finite number of which vanish. By definition, the . . spanned by the set . is the tensor algebra . of the vector space ..
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https://doi.org/10.1007/978-3-8350-9279-2Everywhere in this section we assume by default that . is a field of characteristic zero.
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