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Results tagged with projective-resolution
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user 25659
5
votes
1
answer
432
views
Projective dimension of simple module
Let $R$ be a (not necessarily commutative) ring and $M$ a simple right $R$-module. Then $\mathfrak{m}=Ann(M)$ is a maximal ideal of $R$. It is seems known that
$$
pdim_{R}(M)=pdim_{R_{\mathfrak{m}}}(M …
- 63
1
vote
1
answer
130
views
Projective dimension over hypersurface
Let $R$ be (not necessarily commutative) ring and $S$ a simple right $R$-module. Let $f\in Ann(S)$ be normalizng and a non-zero divisor. Is it always true that
$$
pdim_{R}(S)=pdim_{R/(f)}(S)+1?
$$
- 63