Titlebook: Basic Modern Algebra with Applications; Mahima Ranjan Adhikari,Avishek Adhikari Textbook 2014 Springer India 2014 Functors.Hilbert Basis T

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Actions of Groups, Topological Groups and Semigroups, a group action. For a topological group action on a topological space, this permutation is a homeomorphism and for a Lie group action on a differentiable manifold it is a diffeomorphism. Group actions are used in the proofs of the Counting Principle, Cayley’s Theorem, Cauchy’s Theorem and Sylow The

線

Rings: Introductory Concepts,udy of modern algebra. A group is endowed with only one binary operation while a ring is endowed with two binary operations connected by some interrelations. Fields form a very important class of rings. The concept of rings arose through the attempts to prove Fermat’s last theorem and was initiated

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延期

Vector Spaces,r vector spaces and closely related fundamental concepts, such as linear independence, basis, dimension, linear transformation and its matrix representation, eigenvalue, inner product space, Hilbert space, quadratic form, Jordan canonical form etc., are studied. Such concepts form an integral part o

儀式

Modules, module over .) and also a natural generalization of a vector space (which is a module over a division ring (field)). Many results of vector spaces are generalized in some special classes of modules, such as free modules and finitely generated modules over principal ideal domains. Modules are closel

極為憤怒

Algebraic Aspects of Number Theory, of modern algebra, which are not studied in Chap.?.. In addition, the applications of number theory, particularly those directed towards theoretical computer science, are presented. Number theory has been used in many ways to devise algorithms for efficient computer and for computer operations with