Retracts and Injectives
Canadian mathematical bulletin, Tome 25 (1982) no. 4, pp. 462-467

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

Embedding theorems are employed to show that many important categories do not possess non-trivial retracts or injectives. E.g., the categories of monoids, groups, rings, rings with unity, polynomial identity rings, nilpotent groups, solvable groups, and several varieties of groups.
DOI : 10.4153/CMB-1982-066-9
Mots-clés : 18G05
Feigelstock, Shalom; Klein, Aaron. Retracts and Injectives. Canadian mathematical bulletin, Tome 25 (1982) no. 4, pp. 462-467. doi: 10.4153/CMB-1982-066-9
@article{10_4153_CMB_1982_066_9,
     author = {Feigelstock, Shalom and Klein, Aaron},
     title = {Retracts and {Injectives}},
     journal = {Canadian mathematical bulletin},
     pages = {462--467},
     year = {1982},
     volume = {25},
     number = {4},
     doi = {10.4153/CMB-1982-066-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-066-9/}
}
TY  - JOUR
AU  - Feigelstock, Shalom
AU  - Klein, Aaron
TI  - Retracts and Injectives
JO  - Canadian mathematical bulletin
PY  - 1982
SP  - 462
EP  - 467
VL  - 25
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-066-9/
DO  - 10.4153/CMB-1982-066-9
ID  - 10_4153_CMB_1982_066_9
ER  - 
%0 Journal Article
%A Feigelstock, Shalom
%A Klein, Aaron
%T Retracts and Injectives
%J Canadian mathematical bulletin
%D 1982
%P 462-467
%V 25
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-066-9/
%R 10.4153/CMB-1982-066-9
%F 10_4153_CMB_1982_066_9

[1] 1. Baer, R., Absolute retracts in group theory, Bull. AMS 52 (1946), 510-506. Google Scholar

[2] 2. Baumslag, G., Wreath products and p-groups, Proc. Camb. Phil. Soc. 55 (1959), 224-231. Google Scholar

[3] 3. Berman, G. and Silverman, R. J., Simplicity of near-rings of transformations, Proc. AMS 10 (1959), 456-459. Google Scholar

[4] 4. Bokut, L. A., Some embedding theorems for rings and semigroups, Sibirsk Mat. Z. 4 (1963), 500-518. Google Scholar

[5] 5. Boone, W. W. and Higman, G., An algebraic characterization of groups with soluble word problem, J. Australian Math. Soc. 18 (1974), 41-53. Google Scholar

[6] 6. Cohn, P. M., Simple rings without zero-divisors and Lie division rings, Mathematika 6 (1959), 4-18. Google Scholar

[7] 7. Higman, G., Neumann, B. H. and Neumann, H., Embedding theorems for groups, J. London Math. Soc. 24 (1949), 247-254. Google Scholar

[8] 8. Klein, A., Relations, in categories, Illinois J. Math. 14 (1970), 536-550. Google Scholar

[9] 9. Klein, A., Injectives and simple objects, J. Pure and App. Alg. 15 (1979), 243-245. Google Scholar

[10] 10. Malone, J. J., A near-ring analogue of a ring embedding theorem, J. Alg. 16 (1970), 237-238. Google Scholar

[11] 11. Meldrum, J. D. P., Injective near-ring of modules over Z , Proc. AMS 68 (1978), 16-18. Google Scholar

[12] 12. Neumann, B. H., Adjunction of elements to groups, J. London Math. Soc. 18 (1943), 4-11. Google Scholar

[13] 13. Neumann, B. H. and Neumann, H., Embedding theorems for groups, J. London Math. Soc. 34 (1959), 465-479. Google Scholar

[14] 14. Raphael, R., Injective rings, Comm. in Alg. 1 (1974), 403-414. Google Scholar

Cité par Sources :