Starting with the basic notions and results in algebraic extensions, the authors give an exposition of the work of Galois on the solubility of equations by radicals, including Kummer and Artin-Schreier extensions followed by a Chapter on algebras which contains, among other things, norms and traces of algebra elements for their actions on modules, representations and their characters, and derivations in commutative algebras. The last Chapter deals with transcendence and includes Luroth's theorem, Noether's normalization lemma, Hilbert's Nullstellensatz, heights and depths of prime ideals in finitely generated overdomains of fields, separability and its connections with derivations.

Algebra: Volume 4 - Field Theory

Science & Math

Luthar, L.S.

Passi, I.B.S.

Mathematics

Alpha Science

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.

Algebra: Volume 2 - Rings

Narosa Publishing House

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Books by Luthar, L.S.