Localization of Right Noetherian Rings at Semiprime Ideals
Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1069-1085

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

In [11] and [12] we investigated the process of localization of right Noetherian rings R at prime ideals. We shall now extend these investigations to semiprime ideals N of R.In Section 2 we show that localizing at the injective right R-module E(R/N) is the same as localizing with respect to the multiplicative set
Lambek, J.; Michler, G. Localization of Right Noetherian Rings at Semiprime Ideals. Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1069-1085. doi: 10.4153/CJM-1974-099-4
@article{10_4153_CJM_1974_099_4,
     author = {Lambek, J. and Michler, G.},
     title = {Localization of {Right} {Noetherian} {Rings} at {Semiprime} {Ideals}},
     journal = {Canadian journal of mathematics},
     pages = {1069--1085},
     year = {1974},
     volume = {26},
     number = {5},
     doi = {10.4153/CJM-1974-099-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-099-4/}
}
TY  - JOUR
AU  - Lambek, J.
AU  - Michler, G.
TI  - Localization of Right Noetherian Rings at Semiprime Ideals
JO  - Canadian journal of mathematics
PY  - 1974
SP  - 1069
EP  - 1085
VL  - 26
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-099-4/
DO  - 10.4153/CJM-1974-099-4
ID  - 10_4153_CJM_1974_099_4
ER  - 
%0 Journal Article
%A Lambek, J.
%A Michler, G.
%T Localization of Right Noetherian Rings at Semiprime Ideals
%J Canadian journal of mathematics
%D 1974
%P 1069-1085
%V 26
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-099-4/
%R 10.4153/CJM-1974-099-4
%F 10_4153_CJM_1974_099_4

[1] 1. Faith, C., Orders in semilocal rings, Bull. Amer. Math. Soc. 77 (1971), 960–962. Google Scholar

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

[3] 3. Goldie, A. W., Semiprime rings with maximum condition, Proc. London Math. Soc. 10 (1960), 201–220. Google Scholar

[4] 4. Goldie, A. W., Localization in non-commutative rings, J. Algebra 5 (1967), 89–105. Google Scholar

[5] 5. Goldie, A. W., The structure of Noetherian rings, Springer Verlag, Lecture Notes in Mathematics 246 (1972), 214–321. Google Scholar

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

[7] 7. Heinicke, A. G., On the ring of quotients at a prime ideal of a right Noetherian ring, Can. J. Math. 24 (1972), 703–712. Google Scholar

[8] 8. Lambek, J., Lectures on rings and modules (Waltham, Toronto, London, 1966). Google Scholar

[9] 9. Lambek, J., Torsion theories, additive semantics and rings of quotients, Springer Verlag, Lecture Notes in Mathematics 177 (Berlin, Heidelberg, New York, 1971). Google Scholar

[10] 10. Lambek, J., Bicommutators of nice infectives, J. Algebra 21 (1972), 60–73. Google Scholar

[11] 11. Lambek, J. and Michler, G., The torsion theory at a prime ideal of a right Noetherian ring, J. Algebra 25 (1973), 364–389. Google Scholar

[12] 12. Lambek, J. and Michler, G., Completions and classical localizations of right Noetherian rings, Pacific J. Math. 48 (1973), 133–140. Google Scholar

[13] 13. Lesieur, L. and Croisot, R., Extension au cas non-commutatif d'un théorème de Krull et d'un lemme d*Artin-Rees, J. Reine Angew. Math. 204 (1960) 216–220. Google Scholar

[14] 14. Matlis, E., Infective modules over Noetherian rings, Pacific J. Math. 8 (1958), 511–528. Google Scholar

[15] 15. Matlis, E., Some properties of Noetherian domains of Dimension 1, Can. J. Math. 13 (1967), 569–586. Google Scholar

[16] 16. Michler, G., Right symbolic powers and classical localization in right Noetherian rings, Math. Z. 127 (1972), 57–69. Google Scholar

[17] 17. Small, L., Orders in Artinian rings, J. Algebra 4 (1966), 13–41. Google Scholar

[18] 18. Small, L., Orders in Artinian rings, II, J. Algebra 9 (1968), 266–273. Google Scholar

[19] 19. Small, L., The embedding problem for Noetherian rings, Bull. Amer. Math. Soc. 75 (1969), 147–148. Google Scholar

[20] 20. Walker, C. L. and Walker, E., Quotient categories and rings of quotients, Rocky Mountain J. Math. 2 (1972), 513–555. Google Scholar

Cité par Sources :