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Results tagged with ac.commutative-algebra
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user 30999
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
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Rank of a $ \mathbb{Z}_{p}[[T]] $ module
Let $p$ be a prime and $M$ is a finitely generated $ \mathbb{Z}_{p}[[T]] $ module. Suppose $M[p]$ denotes the $p$-torsion of $M$. Then $M[p]$ and $M/(p)$ are both $ F_{p}$ vector spaces. So we can tal …
- 1,209
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Pontryagin dual
Suppose $M$ is a $Z_p[[T]]$-module and $\widehat{M}$(the Pontryagin dual of $M$) is a finitely generated torsion $Z_p[[T]]$-module. How to prove that $\widehat{M}$ has $\mu$-invariant zero $\Longleftr …
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Iwasawa invariants
Suppose $M$ is a finitely generated torsion $Z_p[[T]]$-module; the torsion comes from the $\mu$-invariant and the $\lambda$-invariant. Consider $M/(p)$ and $M[p]$ ($p$-torsion of $M$) which are $F_p[[ …
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