Stable Module Category

by Lambert M. Surhone - Sold by Dodax
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Lambert M. Surhone Stable Module Category
Lambert M. Surhone - Stable Module Category

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In representation theory, the stable module category is a category in which projectives are "factored out." Let R be a ring. For two modules M and N, define underline{mathrm{Hom}}(M,N) to be the set of R-linear maps from M to N modulo the relation that f~g if f-g factors through a projective module. The stable module category is defined by setting the objects to be the R-modules, and the morphisms are the equivalence classes underline{mathrm{Hom}}(M,N). Given a module M, let P be a projective module with a surjection p colon P to M. Then set (M) to be the kernel of p. Suppose we are given a morphism f colon M to N and a surjection q colon Q to N where Q is projective. Then one can lift f to a map P to Q which maps (M) into (N). This gives a well-defined functor from the stable module category to itself.


Editor Lambert M. Surhone

Editor Mariam T. Tennoe

Editor Susan F. Henssonow

Product Details


GTIN 9786131239663

Language English

Pages 100

Product type Paperback

Dimension 8.66  inches

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