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Results tagged with homological-dimension
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user 2083
For questions having to do with projective and injective dimensions of modules, global dimension of rings and algebras, and related concepts.
12
votes
Accepted
Projective & injective dimensions
To complement Mariano's answer: If finite projective dimension implies finite injective dimension for any module $M$, then $R$ better have finite injective dimension (the converse is also quite easy). …
- 30.6k
2
votes
Projective dimension of a sub-ideal
Interestingly, the equality you seek holds in one important special case. If $I$ is any monomial ideal and $J$ is the radical of $I$, then $pd_S(I)\leq pd_S(J)$. See the proof of Theorem 2.6 in this p …
- 30.6k