Residual Finiteness in Rings and Modules

In [5] J. Lewin showed that there are many similarities between finitely generated (abbreviated as f(g) groups and/ g rings. Based on the work of J. Lewin, in [8] M. Orzech and L. Ribcs obtained many interesting results on residual finiteness and Hopficity in the category of rings. In our present paper, we give some more instances of similarities between/ g groups and/ g rings. Also, we study residual finiteness and Hopficity in module categories. This study has led us to extending the scope of the work of the above mentioned authors.