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Results tagged with ac.commutative-algebra
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user 33289
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
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Length of a module
Let R be a commutative ring, M an R-module of finite length and let N be an Injective R-module with zero socle. Then why $ \text{Hom}_R(M, N) $ is zero?
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About regular local rings and Socles
Let R be a regular local ring with $ \text{dim} R = d $. If $ 0\rightarrow R\rightarrow I_0\rightarrow ...\rightarrow I_d\rightarrow 0 $. Then why for $ 0\leq i\leq d-1 $, the socle of $ I_i $ is zer …
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