Abstract Algebra by A.R. Vasishtha
Requirements: .PDF reader, 7 MB
Overview: SYLLABUS- ABSTRACT ALGEBRA, Section-A
Rings and Fields: Introduction to rings, Integral domains and fields, Characteristic
of a ring, Ring homomorphism, Ideals and quotient rings, Field of quotients of an
integral domain, Euclidean rings. Polynomial rings, Polynomials over the rational
field, Eisenstein’s criteria, Unique factorization domain.
Section-B
Vector spaces: Definition and examples of vector spaces, Subspaces, Sum and direct
sum of subspace, Linear span, Linear dependence, Independence and their basic
properties, Basis Dimension, Existence of complementary subspace of a subspace of a
finite dimensional vector space, Dimensions of sums of subspaces, Quotient space
and its dimension.
Linear transformations and their representations as matrices, The algebra of linear
transformations, The rank — nullity theorem, Change of basis. Dual space, Bidual
space end natural isomorphism.
Application of matrices to a system of linear (both homogeneous and non-homogeneous)
equations, Theorems on consistency of a system of linear equations,
The characteristic equation of a matrix, Eigen values and eigen vectors, Cayley-
Hamilton theorem and its use in finding inverse of a matrix, Diagonalisation of
square matrices with distinct eigen values.
Genre: Non-Fiction > Educational
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