Bulletin of the
Korean Mathematical Society BKMS

The concepts {\it linearly independent elements} and {\it $u$-linearly independent elements} in an $N$-group $G$ where $N$ is a near-ring, were introduced and studied. A few important results in the theory of vector spaces were generalized to $N$-groups.

Keywords: Goldie dimension, uniform ideal, complement, linearly independent elements, essentially spanning subset, $u$-linearly independent elements

MSC numbers: 16A55, 16A66, 16A76