Can anybody suggest a good book on the topics listed below? A single book would be preferable. Thanks.
Groups, subgroups, normal subgroups,cosets,Lagrange’s theorem, rings and their properties, commutative rings, integral domains and fields, subrings, ideals and their elementary properties. Vector spaces, subspaces and their properties,linear independence and dependence of vectors, matrices, rank of a matrix, reduction to normal forms, linear homogeneous and non-homogenous equations, Cayley-Hamilton theorem, characteristic roots and vectors. DeMoivre’s theorem, relation between roots and coefficient of $n$-th degree equation, solution to cubic and biquadratic equations, transformation of equations.