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Retracts and Injectives

Published online by Cambridge University Press:  20 November 2018

Shalom Feigelstock  and
Aaron Klein
Shalom Feigelstock
Affiliation:
Bar-Ilan UniversityRamat-Gan, Israel
Aaron Klein
Affiliation:
Bar-Ilan UniversityRamat-Gan, Israel
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Abstract

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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.

Keywords

18G05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 4 , 01 December 1982 , pp. 462 - 467
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Baer, R., Absolute retracts in group theory, Bull. AMS 52 (1946), 510-506.Google Scholar
2. Baumslag, G., Wreath products and p-groups, Proc. Camb. Phil. Soc. 55 (1959), 224-231.Google Scholar
3. Berman, G. and Silverman, R. J., Simplicity of near-rings of transformations, Proc. AMS 10 (1959), 456-459.Google Scholar
4. Bokut, L. A., Some embedding theorems for rings and semigroups, Sibirsk Mat. Z. 4 (1963), 500-518.Google Scholar
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. Cohn, P. M., Simple rings without zero-divisors and Lie division rings, Mathematika 6 (1959), 4-18.Google Scholar
7. Higman, G., Neumann, B. H. and Neumann, H., Embedding theorems for groups, J. London Math. Soc. 24 (1949), 247-254.Google Scholar
8. Klein, A., Relations, in categories, Illinois J. Math. 14 (1970), 536-550.Google Scholar
9. Klein, A., Injectives and simple objects, J. Pure and App. Alg. 15 (1979), 243-245.Google Scholar
10. Malone, J. J., A near-ring analogue of a ring embedding theorem, J. Alg. 16 (1970), 237-238.Google Scholar
11. Meldrum, J. D. P., Injective near-ring of modules over Zn , Proc. AMS 68 (1978), 16-18.Google Scholar
12. Neumann, B. H., Adjunction of elements to groups, J. London Math. Soc. 18 (1943), 4-11.Google Scholar
13. Neumann, B. H. and Neumann, H., Embedding theorems for groups, J. London Math. Soc. 34 (1959), 465-479.Google Scholar
14. Raphael, R., Injective rings, Comm. in Alg. 1 (1974), 403-414.Google Scholar