In this volume the authors continue their exposition of algebra, begun in Volume 1 with the study of groups, and present some of the basic notions in the theory of rings. The main topics studied are: integral and algebraic elements, rings of matrices, quaternions with applications to SU(2,C) and SO(3,R), rings of endomorphisms, rings of fractions, polynomials and power series, unique factorization, Euclidean and principal ideal domains, ideal theory, finiteness conditions and Dedekind domains. An attractive feature of the book is its richness in purposeful examples and instructive exercises with focus on connections with number theory.
I. S. Luthar.: Retired Professor of Mathematics, Punjab University Chandigarh, India I. B. S. Passi.: Centre for Advanced Study in Mathematics Punjab University, Chandigarh, India
Rings / Matrices and Endomorphisms / Rings of Fractions, Division Rings and Prime Fields / Polynomials / Cayley-Hamilton Theorem / Symmetric Polynomials, Resultant / Power Series / Factorization in Integral Domains / Euclidean and Principal Ideal Domains / Ideals and Homomorphism Theorems / Maximal Ideals / Prime Ideals / Finiteness Conditions / Dedekind Domains / Bibliography / Index.
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- ID: 9788173193132
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