When is Every Kernel Functor Idempotent?
Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 545-554

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Introduction. All rings occurring are associative and possess a unity, which is preserved under subrings and ring homomorphisms. All modules are unitary right modules. We denote the category of rights-modules.In recent years several authors have studied rings R by imposing restrictions on the torsion theories [4] of . (See for instance [2; 23; 24].) This paper offers another alternative to that trend, namely the study of rings R via their set of kernel functors K{R).
Viola-Prioli, Jorge E. When is Every Kernel Functor Idempotent?. Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 545-554. doi: 10.4153/CJM-1975-065-1
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[1] 1. Cartan, H. and Eilenberg, S., Homological algebra (Princeton University Press, Princeton, N.J., 1956). Google Scholar

[2] 2. Cateforis, V. and Sandomierski, F., The singular submodule splits off, J. Algebra 10 (1968), 149–165. Google Scholar

[3] 3. Cozzens, J., Homological properties of the ring of differential polynomials, Bull. Amer. Math. Soc. 76 (1970), 75–79. Google Scholar

[4] 4. Dickson, S., A torsion theory for abelian categories, Trans. Amer. Math. Soc. 121 (1966), 223–235. Google Scholar

[5] 5. Faith, C., A correspondence theorem for projective modules and the structure of simple noetherian rings, Instituto Nazionale di Alta Matematica, Symposia Mathematica, Vol. VIII (1972), 309–345. Google Scholar

[6] 6. Faith, C., Lectures on infective modules and quotient rings, Lecture Notes in Mathematics No. 49 (Springer Verlag, Berlin and New York, 1967). Google Scholar

[7] 7. Faith, C., When are proper cyclics infective. Pacific J. Math. 45 (1973), 97–112. Google Scholar

[8] 8. Faith, C. and Utumi, Y., On noetherian prime rings, Trans. Am. Math. Soc. 114 (1965), 53–60. Google Scholar

[9] 9. Gabriel, P., Des catégories abéliennes, Bull. Soc. Math. France 90 (1962), 323–448. Google Scholar

[10] 10. Gardner, B., Rings whose modules form few torsion classes, Bull. Austral. Math. Soc. 4 (1971), 355–359. Google Scholar

[11] 11. Goldie, A., Semi-prime rings with maximum condition, Proc. Lond. Math. Soc. 10 (1960), 201–220. Google Scholar

[12] 12. Goldman, O., Rings and modules of quotients, J. Algebra 13 (1969), 10–47. Google Scholar

[13] 13. Goodearl, Am. Math. Soc. Memoirs No. Google Scholar

[14] 14. Jacobson, N., Structure of rings (Amer. Math. Soc, Providence, R.I., 1964). Google Scholar

[15] 15. Johnson, R., Quotient rings of rings with zero singular ideal, Pacific J. Math. 11 (1961), 1385–1392. Google Scholar

[16] 16. Kurshan, R., Rings whose cyclic modules have finitely generated socle, J. Algebra 15 (1970), 376–386. Google Scholar

[17] 17. Lambek, J., Lectures on rings and modules (Blaisdell Publishing Co., Waltham Mass., 1966). Google Scholar

[18] 18. Lambek, J., Torsion theories, additive semantics and rings of quotients, Lecture Notes in Mathematics No. 177 (Springer Verlag, Berlin and New York, 1971). Google Scholar

[19] 19. Morita, K., Duality for modules and its application to the theory of rings with minimum condition, Science Reports Tokyo Kyoiku Daigaku, 6 Ser. A, 1958. Google Scholar

[20] 20. Ornstein, A., Ph. D. Thesis, Rutgers University, 1967. Google Scholar

[21] 21. Osofsky, B., On twisted polynomial rings, J. Algebra 18 (1971), 405–414. Google Scholar

[22] 22. Sandomierski, F., Semisimple maximal quotient rings, Trans. Amer. Math. Soc. 128 (1967), 112–120. Google Scholar

[23] 23. Teply, M., Homological dimension and splitting torsion theories, Pacific J. Math. 34 (1970), 193–205. Google Scholar

[24] 24. Teply, M. and Fuelberth, D., The torsion submodule splits off, Math. Ann. 188 (1970), 270–284. Google Scholar

[25] 25. Utumi, Y., On quotient rings, Osaka Math. J. 8 (1956), 1–18. Google Scholar

[26] 26. Zelmanowitz, J., Endomorphism rings of torsionless modules, J. Algebra 5 (1967), 325–341. Google Scholar

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