Geodesic
Type Radicals
Glasgow mathematical journal, Tome 9 (1968) no. 1, pp. 22-29

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

The lower radical of a module type. For a ring R with unit, the module type t(R) was defined in [6] as follows: t(0) = 0; t(R) = d if every free R-module has invariant rank; t(R) = (c, k) for integers c, k ≧ 1 if every free R-module of rank < c has invariant rank, while a free module of rank h ≧ c has rank h + nk for any integer n ≧ 0. The module types form a lattice under the ordering 0 < (c, k) < d and (c', k') ≦ (c, k) if and only if c ' ≦ c and k' I k. Two of the basic theorems on types are:A. [6; Theorem 2, p. 115] If R → R' is a unit-preserving homomorphism, then t(R')≦ t(R). 
Leavitt, W. G. Type Radicals. Glasgow mathematical journal, Tome 9 (1968) no. 1, pp. 22-29. doi: 10.1017/S0017089500000252
@article{10_1017_S0017089500000252,
     author = {Leavitt, W. G.},
     title = {Type {Radicals}},
     journal = {Glasgow mathematical journal},
     pages = {22--29},
     year = {1968},
     volume = {9},
     number = {1},
     doi = {10.1017/S0017089500000252},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500000252/}
}
TY  - JOUR
AU  - Leavitt, W. G.
TI  - Type Radicals
JO  - Glasgow mathematical journal
PY  - 1968
SP  - 22
EP  - 29
VL  - 9
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500000252/
DO  - 10.1017/S0017089500000252
ID  - 10_1017_S0017089500000252
ER  - 
%0 Journal Article
%A Leavitt, W. G.
%T Type Radicals
%J Glasgow mathematical journal
%D 1968
%P 22-29
%V 9
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500000252/
%R 10.1017/S0017089500000252
%F 10_1017_S0017089500000252

[1] 1.Conn, P. M., Some remarks on the invariant basis property, Topology 5 (1966), 215–228. Google Scholar

[2] 2.Dieudonne, J., Sur le nombre de dimensions d'un module, C. R. Acad. Sci. Paris 215 (1942), 563–565. Google Scholar

[3] 3.Hoffman, A. E., The constructions of the general theory of radicals, Thesis, University of Nebraska (1966). Google Scholar

[4] 4.Jacobson, N., The theory of rings, Amer. Math. Soc. Mathematical Surveys, No. 2 (Providence, R.I., 1943). Google Scholar | DOI

[5] 5.Kurosh, A. G., Radicals in rings and algebras, Mat. Sb. N.S. 33 (1953), 13–26. Google Scholar

[6] 6.Leavitt, W. G., The module type of a ring, Trans. Amer. Math. Soc. 103 (1962), 113–130. Google Scholar

[7] 7.Leavitt, W. G., The module type of homomorphic images, Duke Math. J. 32 (1965), 305–312. Google Scholar | DOI

[8] 8.McCoy, N. H., Theory of rings (New York, 1964). Google Scholar

[9] 9.Peinado, R. E. and Leavitt, W. G., The maxit and minit of a ring, Proc. Glasgow Math. Assoc. 7 (1966), 128–135. Google Scholar | DOI

[10] 10.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 | DOI

Cité par Sources :