query: Rank of free submodules of a free module over a commutative ring.
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: 35745
negative_passages.text: Question about a submodule
negative_passages.docid: 32172
negative_passages.text: Homomorphisms of graded modules
negative_passages.docid: 2719
negative_passages.text: Why isn't an infinite direct product of copies of $\Bbb Z$ a free module?
negative_passages.docid: 76501
negative_passages.text: How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?
negative_passages.docid: 104784
negative_passages.text: On the grade of an ideal
negative_passages.docid: 69384
negative_passages.text: Are the following modules free and/or isomorphic?
negative_passages.docid: 128493
negative_passages.text: Given a commutative ring $R$ and an epimorphism of free modules $R^m \to R^n$ is then $m \geq n$?
negative_passages.docid: 17978
negative_passages.text: Isomorphism classes of $\mathbb{Z}[i]$ modules.
negative_passages.docid: 117211
negative_passages.text: Infinite linear independent family in a finitely generated $A$-module
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: 113512
negative_passages.text: Characteristic of nonzero commutative rings with unity
negative_passages.docid: 126472
negative_passages.text: Surjective endomorphisms of uniserial modules
negative_passages.docid: 158142
negative_passages.text: Total space of a finite rank locally free sheaf, Vakil's 17.1.4 & 17.1.G
negative_passages.docid: 70658
negative_passages.text: Isomorphism between quotient modules
negative_passages.docid: 21466
negative_passages.text: $P$ is projective . Show that $P$ is a direct summand of a free $R-$ module
negative_passages.docid: 98155
negative_passages.text: Free products of cyclic groups