Geodesic
Lower Radicals in Associative Rings
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 466-476

Voir la notice de l'article provenant de la source Cambridge University Press

Given a homomorphically closed class of (not necessarily associative) rings , the lower radical property determined by is the least radical property for which all rings in are radical. Recently (7) a process of constructing the lower radical property from a class of associative rings has been given which terminates after a countable number of steps. In this process, an ascending chain of classes is obtained and the property of being a ring in the class is the lower radical property determined by . In Theorem 1 we give another characterization of the rings in the class , λ ∈ {1, 2, ..., omega; 0}, and a procedure for constructing the lower radical determined by in an arbitrary associative ring is given. 
Watters, J. F. Lower Radicals in Associative Rings. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 466-476. doi: 10.4153/CJM-1969-051-3
@article{10_4153_CJM_1969_051_3,
     author = {Watters, J. F.},
     title = {Lower {Radicals} in {Associative} {Rings}},
     journal = {Canadian journal of mathematics},
     pages = {466--476},
     year = {1969},
     volume = {21},
     number = {1},
     doi = {10.4153/CJM-1969-051-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-051-3/}
}
TY  - JOUR
AU  - Watters, J. F.
TI  - Lower Radicals in Associative Rings
JO  - Canadian journal of mathematics
PY  - 1969
SP  - 466
EP  - 476
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-051-3/
DO  - 10.4153/CJM-1969-051-3
ID  - 10_4153_CJM_1969_051_3
ER  - 
%0 Journal Article
%A Watters, J. F.
%T Lower Radicals in Associative Rings
%J Canadian journal of mathematics
%D 1969
%P 466-476
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-051-3/
%R 10.4153/CJM-1969-051-3
%F 10_4153_CJM_1969_051_3

[1] 1. Anderson, T., Divinsky, N., and Sulinski, A., Hereditary radicals in associative and alternative rings, Can. J. Math. 17 (1965), 594–603. Google Scholar

[2] 2. Andrunakievic, V. A., Radicals in associative rings (1) Mat. Sb. (N.S.) U (1958), 179-212 = Amer. Math. Soc. Transi., Ser. 2, 1966, Vol. 52, pp. 95–128. Google Scholar

[3] 3. Armendariz, E. P. and Leavitt, W. G., The hereditary property in the lower radical construction, Can. J. Math. 20 (1968), 474–476. Google Scholar

[4] 4. Fuchs, L., Abelian groups (Pergamon, New York, 1960). Google Scholar

[5] 5. Heinicke, A. G., A note on lower radical constructions for associative rings, Can. Math. Bull. 11 (1968), 23–30. Google Scholar

[6] 6. Michler, G., Radikale und Sockel, Math. Ann. 167 (1966), 1–48. Google Scholar

[7] 7. Sulinski, A., Anderson, R., and Divinsky, N., Lower radical properties for associative and alternative rings, J. London Math. Soc. 41 (1966), 417–424. Google Scholar

Cité par Sources :