CLASS OF NILARY RINGS AND GROUP RINGS

Abstract

ABSTRACT: Let A be a ring with unity and let G be a group. For the group ring A[G]; we proved that: (1) if A[G] is a (p-) nilary ring, then the ring A is a (p-) nilary ring; (2) if A is a (p-)nilary ring, G is a finite p-group and p is nilpotent in A; then A[G] is a (p-)nilary ring; (3) if A is a prime ring, (G) = G is a p-group, and p = 0 in A; then A[G] is a p-nilary ring; (4) if A[G] is (p-)nilary, then either G is a prime group or jHj is nilpotent in A for any nontrivial finite normal subgr