Algebra

From rings to modules to groups to fields this undergraduate introduction to abstract algebra follows an unconventional path. The text emphasizes a modern perspective on the subject with gentle mentions of the unifying categorical principles underlying the various constructions and the role of universal properties. A key feature is the treatment of modules including a proof of the classification theorem for finitely generated modules over Euclidean domains. Noetherian modules and some of the language of exact complexes are introduced. In addition standard topics - such as the Chinese Remainder Theorem the Gauss Lemma the Sylow Theorems simplicity of alternating groups standard results on field extensions and the Fundamental Theorem of Galois Theory - are all treated in detail. Students will appreciate the text''s conversational style 400+ exercises an appendix with complete solutions to around 150 of the main text problems and an appendix with general background on basic logic and nave set theory.