This ebook is designed as a textual content for a first-year graduate algebra direction. As beneficial historical past we'd think of a great undergraduate linear algebra direction. An undergraduate summary algebra path, whereas important, isn't valuable (and so an adventurous undergraduate may perhaps examine a few algebra from this book). might be the vital distinguishing function of this e-book is its standpoint. Many textbooks are typically encyclopedic. we now have attempted to put in writing person who is thematic, with a constant viewpoint. The subject, as indicated through our name, is that of modules (though our goal has now not been to jot down a textbook in simple terms on module theory). we commence with a few crew and ring conception, to set the level, after which, within the center of the publication, boost module conception. Having constructed it, we current a few of its functions: canonical kinds for linear alterations, bilinear varieties, and workforce representations. Why modules? the answer's that they're a uncomplicated unifying thought in arithmetic. The reader is maybe already conversant in the fundamental function that vector areas play in arithmetic, and modules are a generalizaÂ­ tion of vector areas. (To be specified, modules are to earrings as vector areas are to fields.

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