This e-book is designed as a textual content for a first-year graduate algebra path. As precious heritage we might contemplate an outstanding undergraduate linear algebra path. An undergraduate summary algebra path, whereas useful, isn't really valuable (and so an adventurous undergraduate may well research a few algebra from this book). might be the valuable distinguishing function of this booklet is its perspective. Many textbooks are typically encyclopedic. now we have attempted to write down one who is thematic, with a constant viewpoint. The topic, as indicated via our name, is that of modules (though our goal has no longer been to jot down a textbook merely on module theory). we commence with a few workforce and ring idea, to set the degree, after which, within the middle of the e-book, strengthen module thought. Having built it, we current a few of its purposes: canonical varieties for linear alterations, bilinear varieties, and workforce representations. Why modules? the answer's that they're a simple unifying inspiration in arithmetic. The reader is maybe already conversant in the fundamental position that vector areas play in arithmetic, and modules are a generaliza­ tion of vector areas. (To be designated, modules are to earrings as vector areas are to fields.

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