## A note on algebraic analogs of the cones spectrum

**Abstract**

COMMUNICATIONS IN ALGEBRA, 19(4), 1249-1270 A Note on ALGEBRAIC ANALOGS of the CONNES SPECTRUM M. Parvathi and Ram Parkash Sharma Ramanujan Institute for Advanced Study in Mathematics University of Madras Madras - 600 005 I NDI A I NTRODUCTI ON In C 61. S. Montgomery and D. S. Passman proved that the Connes subgroup r is equal to the orthogonal complement of the split center H of the group G , when the ring R is prime and G is abelian . In this paper, using the results of V. K Kharchenko 12,31 , we establish the same relation between and H , when R is G-pr i me and G is abel ian . 1 . PRELI MI NARI ES Throughout this paper R is a K-algebra with 1 , where K is a field with I . Let G be a finite abelian group with 1 , acting on R as K-algebra autornorphisms . We assume that \GI-' E K and K contains all nth roots of unity . n is equal to the order of G . Let G = Horn C G,K 1 be the dual of G . As shown in C61 , R