## Prime kernel functors of group graded rings and smash products

**Abstract**

COMMUNICATIONS IN ALGEBRA, 17(7), 1535-1563 (1989) PRIME KERNEL FUNCTORS OF GROUP GRADED RINGS AND SMASH PRODUCTS M. Par vathi and Ram Par kash Shar ma The Ramanujan Institute for Advced Study in Mathematics Uni ver si t y of Madras Madras - 600 005 I ndi a Introduction. In 161 M.Lorenz and D.S.Passman studied the relations between the set of prime ideals of the ring R and its crossed product Re . M. Cohen and S. Montgomery C11 obtained results similar to C61 for prime ideals of the group graded ring R and its smash product R#KCGl . The results of C61 are extended in C71 and C81 to prime kernel functors of a ring R and its skew group ring RIcG both having Gabriel dimension . Here we extend the results of C11 to prime kernel functors of the graded ring R , having Gabriel dimension , and R#KEGI* . Copyright @ 1989 by Marcel Dekker, Inc. 1536 PARVATHI AND PARKASH SHARMA 1 Preliminaries. Let R be a K-algebra with 1 . over a commutative ring K with 1 and G be a finite group with 1 such that the order of G is a unit in R