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Advanced Modern Algebra (Graduate Studies in Mathematics) by Joseph J. Rotman is a nonfiction available to read on EtoBox.

What is Advanced Modern Algebra (Graduate Studies in Mathematics) about?

"This book is designed as a text for the first year of graduate algebra, but it can also serve as a reference since it contains more advanced topics as well. This second edition has a different organization than the first. It begins with a discussion of the cubic and quartic equations, which leads into permutations, group theory, and Galois theory (for finite extensions; infinite Galois theory is discussed later in the book). The study of groups continues with finite abelian groups (finitely generated groups are discussed later, in the context of module theory), Sylow theorems, simplicity of projective unimodular groups, free groups and presentations, and the Nielsen-Schreier theorem (subgroups of free groups are free). The study of commutative rings continues with prime and maximal ideals, unique factorization, noetherian rings, Zorn's lemma and applications, varieties, and Gröbner bases. Next, noncommutative rings and modules are discussed, treating tensor product, projective, injective, and flat modules, categories, functors, and natural transformations, categorical constructions (including direct and inverse limits), and adjoint functors. Then follow group representations: Wed

Who reads Advanced Modern Algebra (Graduate Studies in Mathematics)?

Author

Joseph J. Rotman

Publisher

American Mathematical Society; Brand: American Mathematical Society

Published

2010

Language

EN

ISBN

9786119551978

Category

nonfiction

Subjects

Mathematics, Algebra, Stem