Abstract
LetG be a group andA aG-graded ring. A (graded) idealI ofA is (graded) essential ifI⊃J≠0 wheneverJ is a nonzero (graded) ideal ofA. In this paper we study the relationship between graded essential ideals ofA, essential ideals of the identity componentA e and essential ideals of the smash productA#G *. We apply our results to prime essential rings, irredundant subdirect sums and essentially nilpotent rings.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Beattie, M. and Stewart, P.,Graded radicals of graded rings, Acta. Mach. Hung., to appear.
Beattie, M. and Stewart, P.,Graded versions of radicals, preprint.
Beattie, M., S.-X., Liu, and Stewart, P.,Comparing graded versions of the prime radical, preprint.
Cohen, M. and Montgomery, S.,Group graded rings, smash products and group actions, Trans. Amer. Math. Soc.,282 (1984), 237–258.
Fisher, J.W.,On the nilpotency of nil subrings, Can. J. Math.,22 (1970), 1211–1216.
Gardner, B.J., and Stewart, P.N.,Prime essential rings, Proc. Edinburgh Math. Soc., to appear.
Levy, L.,Unique subdirect sums of prime rings, Trans. Amer. Math. Soc.,106 (1963), 64–76.
S.-X. Liu,Two results on smash products, Kexue Tongbao, 34:13 (1989), 967-969.
Passman, D.S.,Semiprime and prime crossed products, J. Alg.,83 (1983), 158–178.
Rowen, L.H.,A subdirect decomposition of semiprime rings and its application to maximal quotient rings, Proc. Amer. Math. Soc.,46 (1974), 176–180.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hongjin, F., Stewart, P. Graded rings and essential ideals. Acta Mathematica Sinica 9, 344–351 (1993). https://doi.org/10.1007/BF02560128
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02560128