Download E-books Algebra: An Approach via Module Theory (Graduate Texts in Mathematics) PDF

By William A. Adkins

This booklet is designed as a textual content for a first-year graduate algebra path. As precious historical past we might contemplate an outstanding undergraduate linear algebra path. An undergraduate summary algebra path, whereas valuable, isn't really helpful (and so an adventurous undergraduate may examine a few algebra from this book). might be the valuable distinguishing function of this ebook is its standpoint. Many textbooks are typically encyclopedic. we've attempted to write down one who is thematic, with a constant standpoint. The topic, as indicated through our name, is that of modules (though our goal has no longer been to write down a textbook basically on module theory). we commence with a few crew and ring thought, to set the degree, after which, within the center of the publication, advance module idea. Having built it, we current a few of its purposes: canonical kinds for linear differences, bilinear varieties, and team representations. Why modules? the answer's that they're a easy unifying notion in arithmetic. The reader is perhaps already conversant in the elemental position that vector areas play in arithmetic, and modules are a generaliza­ tion of vector areas. (To be special, modules are to earrings as vector areas are to fields.

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