Let $R$ be a ring and $R^n$ be the external sum of $n$ copies of the $R$-module $R$. Let's take $t$ elements of our $R$-module $R^n$ and call $M$ the sub-module generated by them. Then call $r$ the maximum number of independent elements among these $t$ elements. Taking such a subset $S$ of $t$ independent elements, it is not always true that $S$ spans $M$ (it is not always true that $M$ is free over $S$). If we take as $R$ a PID, then can such an unpleasant situations happen?
2026-04-05 22:15:51.1775427351
Question about modules
32 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in MODULES
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