This book is designed for robust undergraduates or early-stage graduate students seeking challenges in abstract algebra. It serves as a valuable supplement to coursework or for those engaged in self-study. Offering a greater range and complexity of problems compared to typical algebra textbooks, it caters to students looking to enhance their mathematical understanding by tackling problems that demand thoughtful consideration and effort.
The content covers problems related to groups (encompassing Sylow Theorems, solvable groups, group presentation by generators and relations, and the structure and duality of finite abelian groups); rings (including fundamental ideal theory and factorization in integral domains, along with Gauss’s Theorem); linear algebra (with a focus on linear transformations, including canonical forms); and fields (incorporating Galois theory). Hints for many problems are provided to aid in the learning process. This resource is suitable for those aiming to deepen their grasp of abstract algebra through engaging and challenging problem-solving exercises.
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