21 mar. 2015

Ring Theory - Louis Rowen Vol. 1 1988

The theory of rings originally developed as a collection of brilliant insights for proving and improving diverse theorems in algebra, by extracting the essence of the theorems divested of superfluous hypotheses. This approach was startlingly successful and led to the search for solutions from “first principles”;
moreover, there was a unifying structure theory due principally to Jacobson, and his book Structure of Rings (1956, rev. 1964) remains one of the principal references in the literature. (The other classic references are Herstein’s Carus Monograph Noncommutative Rings and, for the homological point of view, Cartan- Eilenberg’s book Homological Algebra.) However, as more and more “elementary” proofs found their way into the folklore, the structure of rings began to resemble a tower of Babel, where ring theorists speak such diverse languages (ring theory, module theory, category theory, etc.) that at times we cannot communicate effectively with one another.

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