# Abstract Algebra Manual

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This is the most current textbook in teaching the basic concepts of abstract algebra. The author finds that there are many students who just memorise a theorem without having the ability to apply it to a given problem. Therefore, this is a hands-on manual, where many typical algebraic problems are provided for students to be able to apply the theorems and to actually practice the methods they have learned. Each chapter begins with a statement of a major result in Group and Ring Theory, followed by problems and solutions. Contents: Tools and Major Results of Groups; Problems in Group Theory; Tools and Major Results of Ring Theory; Problems in Ring Theory; Index.Solution: Let M be a maximal ideal of R. Since M is a subgroup (under addition) of R, we conclude that Ord(M) = p OR 1. Since M # R, Ord(M) = 1. ... It is clear that \$ is one-to-one, and thus I is ONTO because Ord(R) = Ord(Zp). Hence RSiZp.

 Title : Abstract Algebra Manual Author : Ayman Badawi Publisher : Nova Publishers - 2004-01-01