Download Algebra II: Textbook for Students of Mathematics by Alexey L. Gorodentsev PDF

By Alexey L. Gorodentsev

This e-book is the second one quantity of a radical “Russian-style” two-year undergraduate direction in summary algebra, and introduces readers to the elemental algebraic buildings – fields, jewelry, modules, algebras, teams, and different types – and explains the most rules of and strategies for operating with them.

The path covers immense parts of complicated combinatorics, geometry, linear and multilinear algebra, illustration thought, class conception, commutative algebra, Galois thought, and algebraic geometry – subject matters which are usually ignored in general undergraduate courses.

This textbook is predicated on classes the writer has performed on the autonomous collage of Moscow and on the school of arithmetic within the greater tuition of Economics. the most content material is complemented via a wealth of workouts for sophistication dialogue, a few of which come with reviews and tricks, in addition to difficulties for self reliant study.

Show description

Read Online or Download Algebra II: Textbook for Students of Mathematics PDF

Best algebra & trigonometry books

Stochastic calculus: a practical introduction

This compact but thorough textual content zeros in at the elements of the idea which are rather suitable to functions . It starts with an outline of Brownian movement and the linked stochastic calculus, together with their courting to partial differential equations. It solves stochastic differential equations by way of various equipment and reviews intimately the one-dimensional case.

Multivariate Approximation and Applications

Approximation thought within the multivariate atmosphere has many functions together with numerical research, wavelet research, sign processing, geographic info structures, laptop aided geometric layout and special effects. This complicated creation to multivariate approximation and comparable issues comprises 9 articles written through top specialists surveying a few of the new rules and their functions.

Almost Free Modules: Set-Theoretic Methods

This is often a longer remedy of the set-theoretic suggestions that have reworked the examine of abelian staff and module idea during the last 15 years. a part of the e-book is new paintings which doesn't seem in different places in any shape. furthermore, a wide physique of fabric which has seemed formerly (in scattered and infrequently inaccessible magazine articles) has been generally remodeled and in lots of circumstances given new and more advantageous proofs.

Extra resources for Algebra II: Textbook for Students of Mathematics

Example text

V; : : : ; VI U/ for the subspace of alternating n-linear maps. Associated with every alternating n-linear map ' W V V V ! U; W/ ! V; W/; F 7! 11) is an isomorphism for all vector spaces W. , , and verify that the target spaces of every two universal symmetric n-linear maps are isomorphic by means of the unique linear map commuting with the s-commutative multiplication. V; / of alternating n-linear forms V V V !  are canonically dual to each other. 2 on p. 28. i1 ; i2 ; : : : ; in / with 1 6 i1 < i2 < dim ƒn V D dn and dim ƒV D 2d .

9) where the right dotted fragments in both decomposable tensors are the same, as are the left dotted fragments as well. The whole ideal sym is the direct sum of these homogeneous components: sym D ˚ sym \ V ˝n : n>0 The quotient algebra SV ≝ TV=sym is called the symmetric algebra of the vector space V. The multiplication in SV is induced by the tensor multiplication in TV and denoted by the dot sign , which is, however, usually omitted. 8) force all vectors u; w 2 V to commute in SV. sym \ V ˝n /: n>0 The space Sn V is called the nth symmetric power of V.

2). 2 Partial Contractions Given a pair of injective but not necessarily order-preserving maps f1; 2; : : : ; pg 1 See Sect. 2 of Algebra I. I J - f1; 2; : : : ; mg ,! j1 ; j2 ; : : : ; jm / for the sequences of their values i D I. /, j D J. /. p m/ ˝ V ˝q ! 6) j…J obtained by contracting the i th tensor factor of V ˝p with the j th tensor factor of V ˝q for D 1; 2; : : : ; m and leaving all the other tensor factors in their initial order. 5) even if the maps have equal images and differ only in the order of sequences i1 ; i2 ; : : : ; im and j1 ; j2 ; : : : ; jm .

Download PDF sample

Rated 4.60 of 5 – based on 47 votes