query: On the $R$-linear independence of free $R$-module
positive_passages.docid: 28136
positive_passages.text: $A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$
negative_passages.docid: 127044
negative_passages.text: Prove that a finitely-generated free module has a finite basis
negative_passages.docid: 123130
negative_passages.text: Showing an isomorphism between exterior products of a free module
negative_passages.docid: 145039
negative_passages.text: Algebraic independence over $\overline{\mathbb Q}$ and over $\mathbb Q$
negative_passages.docid: 36987
negative_passages.text: A criterion of flat modules
negative_passages.docid: 51313
negative_passages.text: Extension of linearly independent set to a basis in an infinite dimensional vector space
negative_passages.docid: 141149
negative_passages.text: Proof some module is direct sum by its submodules.
negative_passages.docid: 102529
negative_passages.text: Prove that the set $\left\{ x, Ax, \dots, A^{k-1} x \right\}$ is linearly independent
negative_passages.docid: 134294
negative_passages.text: A (not necessarily unitary) $R$ module $M$ splits into $B\oplus C$ where $B$ is unitary and $RC=\{0\}$.
negative_passages.docid: 140340
negative_passages.text: Left and right R-modules
negative_passages.docid: 111307
negative_passages.text: If ideal $I$ of domain $R$ is free $R$-module, then $I$ is principal ideal.
negative_passages.docid: 94077
negative_passages.text: Proof of linear independence of $e^{at}$
negative_passages.docid: 138343
negative_passages.text: How to prove that the set $\{\sin(x),\sin(2x),...,\sin(mx)\}$ is linearly independent?
negative_passages.docid: 37953
negative_passages.text: Primary Decomposition of $\mathbb{R^n}$ under T
negative_passages.docid: 122387
negative_passages.text: Is a stably free module always free?
negative_passages.docid: 145758
negative_passages.text: Are submodules of finitely generated free modules always free?
negative_passages.docid: 144122
negative_passages.text: A problem about an $R$-module that is both injective and projective.