Abstract
The relationship between the radical of a ringR and a structural matrix ring overR has been determined for some radicals. We continue these investigations, amongst others, determining exactly which radicals γ have the property γ(M(ρ,R))=M(ρ s ,γ(R))+M(ρ a ,γ+(R))for any structural matrix ringM(ρ,R) and finding β(M(ρ,R)) for any hereditary subidempotent radical β.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
De La Rosa, B.: A radical class which is fully determined by a lattice isomorphism. Acta Sci. Math. (Szeged)33, 337–341 (1972).
Gardner, B. J.: Radicals of abelian groups and associative rings. Acta Math. Acad. Sci. Hungar.24, 259–268 (1973).
Gardner, B. J.: Some aspects of T-nilpotence. Pacific J. Math.53, 117–130 (1974).
Groenewald, N. J., Van Wyk, L.: Polynomial regularities in structural matrix rings. Comm. Algebra22, 2101–2123 (1994).
Jaegermann, M., Sands, A. D.: On normal radicals, N-radicals and A-radicals. J Algebra50, 337–349 (1978).
Sands, A. D.: Radicals of structural matrix rings. Quaest. Math.13, 77–81 (1990).
Van Wyk, L.: Subrings of Matrix Rings. Ph.D. thesis. University of Stellenbosch 1986.
Van Wyk, L.: Maximal left ideals in structural matrix rings. Comm. Algebra16, 399–419 (1988).
Van Wyk, L.: Special radicals in structural matrix rings. Comm. Algebra16, 421–435 (1988).
Wiegandt, R.: Radical and Semisimple Classes of Rings. Queen's papers in pure and applied mathematics, 37, Kingston, Ontario, 1974.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Veldsman, S. On the radicals of structural matrix rings. Monatshefte für Mathematik 122, 227–238 (1996). https://doi.org/10.1007/BF01320186
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01320186