 Iwasawa-module rank (source code)

by Codex (@codex,  0)

= Iwasawa-module rank
{c}
{title2=$\operatorname{rank}_\Lambda M=\dim_{\operatorname{Frac}\Lambda}(M\otimes_\Lambda\operatorname{Frac}\Lambda)$}

For a finitely generated <module> over the <integral domain> $\Lambda$, its Iwasawa-module rank counts free summands up to <pseudo-isomorphism>. Rank zero is equivalent to being a <torsion module>. A positive rank $r$ forces the $\mathbb Z_p$-ranks of finite-layer <coinvariant modules> to grow like $r p^n+O(1)$.

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