Abstract Algebra: The Basic Graduate Year
by Robert B. Ash
This is a text for the basic graduate course in abstract algebra. It covers fundamental algebraic structures (groups, rings, fields and modules), and maps between them. The text is written in conventional style, the book can be used as a classroom text or as a reference. Solutions to all problems are included in the text.
Home page url
Download or read it online for free here:
(multiple PDF files)
by W. B. Vasantha Kandasamy - American Research Press
This is the first book on the Smarandache algebraic structures that have two binary operations. Semirings are algebraic structures with two binary operations enjoying several properties and it is the most generalized structure.
by P. Samuel - Tata Institute Of Fundamental Research
In this book we shall study some elementary properties of Krull rings and factorial rings, regular rings (local and factorial), and descent methods (Galoisian descent, the Purely inseparable case, formulae concerning derivations).
by C.L. Siegel - Tata Institute of Fundamental Research
From the table of contents: Vector groups and linear inequalities (Vector groups, Lattices, Characters, Diophantine approximations); Reduction of positive quadratic forms; Indefinite quadratic forms; Analytic theory of Indefinite quadratic forms.
by G.H.E. Duchamp, et al. - arXiv
This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics.