A note on dimensions in N-groups

The concepts essential and finite dimension played an important role in the development of the dimension theory of modules over rings. Finite dimension, essential, strictly essential, and some related concepts were studied in nearrings and N-groups by Reddy-Satyanarayana [11], Satyanarayana [14, 20], Satyanarayana-Syam Prasad [22, 23, 24, 25]. In this paper, the authors introduced the concept finite 1-dimension and studied the relationship between finite dimension and finite 1-dimension. Some related examples are also provided.