query: What are all the $k$-dimensional unimodular subspaces of $\mathbb{Z}^n$?
positive_passages.docid: 143069
positive_passages.text: What are the direct summands in $\mathbb{Z}^n$?
negative_passages.docid: 73690
negative_passages.text: If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $
negative_passages.docid: 133019
negative_passages.text: Nilpotent elements in $\mathbb Z_n$
negative_passages.docid: 70543
negative_passages.text: Does an uncountable discrete subspace of the reals exist?
negative_passages.docid: 19396
negative_passages.text: For subspaces, if $N\subseteq M_1\cup\cdots\cup M_k$, then $N\subseteq M_i$ for some $i$?
negative_passages.docid: 92211
negative_passages.text: When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?
negative_passages.docid: 74764
negative_passages.text: Dimension for a closed subspace of $C[0,1]$.
negative_passages.docid: 67772
negative_passages.text: How to find $k$ such that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_k$
negative_passages.docid: 74465
negative_passages.text: One-dimensional vector space and it's subspaces
negative_passages.docid: 125073
negative_passages.text: Finite-dimensional subspaces of normed vector spaces are direct summands
negative_passages.docid: 13761
negative_passages.text: Automorphisms in $\mathbb{Z}_n$
negative_passages.docid: 35034
negative_passages.text: Multiplicative inverses for $Z_n$
negative_passages.docid: 146143
negative_passages.text: Question about proof that finite-dimensional subspaces of normed vector spaces are direct summands
negative_passages.docid: 79061
negative_passages.text: show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
negative_passages.docid: 93263
negative_passages.text: Can contractible subspace be ignored/collapsed when computing $\pi_n$ or $H_n$?
negative_passages.docid: 102112
negative_passages.text: Idempotents in $\mathbb Z_n$
negative_passages.docid: 107000
negative_passages.text: Dimension of intersection of distinct subspaces