Self-orthogonal Modules of Finite Projective Dimension
نویسندگان
چکیده
Let R be a ring and R a self-orthogonal module. We introduce the notion of the right orthogonal dimension (relative to R ) of modules. We give a criterion for computing this relative right orthogonal dimension of modules. For a left coherent and semilocal ring R and a finitely presented self-orthogonal module R , we show that the projective dimension of R and the right orthogonal dimension (relative to R ) of R/J are identical, where J is the Jacobson radical of R. As a consequence, we get that R has finite projective dimension if and only if every left (finitely presented) R-module has finite right orthogonal dimension (relative to R ). If is a tilting module, we then prove that a left R-module has finite right orthogonal dimension (relative to R ) if and only if it has a special ⊥-preenvelope.
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تاریخ انتشار 2008