Titlebook: Rings and Categories of Modules; Frank W. Anderson,Kent R. Fuller Textbook 19741st edition Springer Science+Business Media New York 1974 A

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Classical Ring-Structure Theorems,hful left module. In Section 14 we study rings characterized by this latter property—the “(left) primitive” rings. Here we prove Jacobson’s important generalization of the semisimple case characterizing left primitive rings as “dense rings” of linear transformations.

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Textbook 19741st editionfor introductory and more advanced graduate courses. We assume the famil- iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-side

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Equivalence and Duality for Module Categories, simple artinian if and only if the category .M is “the same” as the category .M for some division ring .. On the other hand, if . is a division ring, then the theory of duality from elementary linear algebra asserts that the categories .FM and FM. of finitely generated left .-vector spaces and right .-vector spaces are “duals” of one another.