Algebra, Vol. 2

Continuing their exposition of algebra begun in Volume 1, in this book the authors present the complexities associated with the study of groups. The main topics studied are: integral and algebraic elements, rings of matrices, quaternions with applications to SU (2,C) and SO (3,R) as well as the rings of endomorphisms and fractions and ideal theory. As with its predecessor, this volume is filled with supportive material including purposeful examples and instructive exercises with a focus on the connections with number theory.

Table of Contents

• 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.

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