In mathematics, especially representation theory, the stable module category is a quotient of a module category in which projectives are "factored out." == Definition == Let R be a ring. For two modules M and N over R, define H o m _ ( M , N ) {\displaystyle {\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.
In mathematics, especially representation theory, the stable module category is a quotient of a module category in which projectives are "factored out." == Definition == Let R be a ring. For two modules M and N over R, define H o m _ ( M , N ) {\displaystyle {\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.
Source: Wikipedia "Stable module category" · CC BY-SA 4.0
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