On Linear Dependence of Rows and Columns in Matrices over Non-commutative Domains

Some well-known correspondences between sets of linearly independent rows and columns of matrices over fields carry over to matrices over non-commutative rings without nontrivial zero divisors.

Automated summary

This statement discusses the applicability of well-known correspondences between sets of linearly independent rows and columns of matrices over non-commutative rings without nontrivial zero divisors.