Titlebook: Noncommutative Algebra; Benson Farb,R. Keith Dennis Textbook 1993 Springer Science+Business Media New York 1993 K-theory.algebra.commutati

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Graduate Texts in Mathematicshttp://image.papertrans.cn/n/image/667186.jpg

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978-1-4612-6936-6Springer Science+Business Media New York 1993

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The Jacobson RadicalIn Chapter One we developed a structure theory for semisimple rings, as summarized in Theorem 1.18. This theory used, for the most part, properties of modules over a semisimple ring in order to characterize such a ring. In this chapter, we give a more intrinsic characterization of semisimple rings.

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The Global Dimension of a Ringn Chapters 1 and 2 can be considered the zero’th step in the theory of global dimension. Kaplansky, based upon an observation of Schanuel, was the first to set down the dimension theory of rings in an elementary way, without using the powerful machinery of homological algebra. This section is based on his Queen Mary College notes.

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