query: counter example of a free module whose rank is less than the number of linearly independent elements
positive_passages.docid: 155799
positive_passages.text: What would be an example of free module such that cardinality of linearly independent set is greater than the rank?
negative_passages.docid: 146664
negative_passages.text: The union of two linearly independent subsets
negative_passages.docid: 86724
negative_passages.text: Example of a non-zero module that has no associated primes
negative_passages.docid: 79591
negative_passages.text: Exact Sequences of Modules and Rank
negative_passages.docid: 40996
negative_passages.text: Proving that free modules are flat (without appealing projective modules)
negative_passages.docid: 3327
negative_passages.text: Height and minimal number of generators of an ideal
negative_passages.docid: 4624
negative_passages.text: Example of a finitely generated module with submodules that are not finitely generated
negative_passages.docid: 140711
negative_passages.text: Linear independence of images by $A$ of vectors whose span trivially intersects $\ker(A)$
negative_passages.docid: 101095
negative_passages.text: Constructing an example s.t. $\operatorname{Hom}_R(M,N)$ is not finitely generated
negative_passages.docid: 158426
negative_passages.text: Proving lemma about centrality of idempotent elements in a Ring with no nilpotent elements.
negative_passages.docid: 141802
negative_passages.text: Prove that free modules are projective
negative_passages.docid: 148828
negative_passages.text: Submodule of a free module
negative_passages.docid: 70298
negative_passages.text: Are quotients of chain groups $C_n(X)/C_n(A)$ still free?
negative_passages.docid: 80616
negative_passages.text: A ring with few invertible elements
negative_passages.docid: 114640
negative_passages.text: Showing that an ideal is not a free $R-$module.
negative_passages.docid: 94203
negative_passages.text: Examples for almost-semirings without absorbing zero
negative_passages.docid: 16275
negative_passages.text: Example of a simple module which does not occur in the regular module?