26- https://doi.org/10.1007/978-1-4612-4418-9_7
Equivalence and Duality for Module Categories
- Jan 1, 1992
- Frank W Anderson +1 more
Abstract
So far our emphasis has been on studying rings in terms of the module categories they admit—that is, in terms of the representations of the rings as endomorphism rings of abelian groups. As we shall see the Wedderburn Theorem for simple artinian rings can be interpreted as asserting that a ring R is simple artinian if and only if the category R M is “the same” as the category D M for some division ring D. On the other hand, if D is a division ring, then the theory of duality from elementary linear algebra asserts that the categories D FM and FM D of finitely generated left D-vector spaces and right D-vector spaces are “duals” of one another.
- # Endomorphism Rings Of Abelian Groups
- # Simple Artinian
- # Division Ring
- # Theory Of Duality
- # Theorem For Rings
- # Rings Of Groups
- # Simple Rings
- # Elementary Algebra
- # Simple Artinian Rings
- # Elementary Linear Algebra
