no. 1
Sur les Extensions Triviales Commutatives
[On Commutative Trivial extensions]
Farid Kourki1
1Département de Mathématiques et Informatique Université Abdelmalek Essaâdi Faculté des Sciences, B.P. 2121 Tétouan, Maroc
Annales mathématiques Blaise Pascal, Volume 16 (2009) no. 1, pp. 139-150

Nous caractérisons les extensions triviales semiGoldie, de cogénération finie, mininjectives et quasi-Frobeniusiens. Comme application, nous montrons que tout anneau noethérien s’injecte dans un anneau quasi-Frobeniusien.

We characterize semiGoldie, finitely cogenerated, mininjective and quasi-Frobenius trivial extensions. As application, we obtain that every nœtherian ring can be embedded in a quasi-Frobenius Ring.

DOI: 10.5802/ambp.260
Classification: 13B99, 13C05, 13C13
Mots-clés : Extensions triviales, SemiGoldie, Mininjectif, Quasi-Frobeniusien
Keywords: Trivial extensions, SemiGoldie, Mininjective, Quasi-Frobenius

Farid Kourki  1

1 Département de Mathématiques et Informatique Université Abdelmalek Essaâdi Faculté des Sciences, B.P. 2121 Tétouan, Maroc 
Farid Kourki. Sur les Extensions Triviales Commutatives. Annales mathématiques Blaise Pascal, Volume 16 (2009) no. 1, pp. 139-150. doi: 10.5802/ambp.260
@article{AMBP_2009__16_1_139_0,
     author = {Farid Kourki},
     title = {Sur les {Extensions} {Triviales} {Commutatives}},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {139--150},
     year = {2009},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {16},
     number = {1},
     doi = {10.5802/ambp.260},
     mrnumber = {2514534},
     language = {fr},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.260/}
}
TY  - JOUR
AU  - Farid Kourki
TI  - Sur les Extensions Triviales Commutatives
JO  - Annales mathématiques Blaise Pascal
PY  - 2009
SP  - 139
EP  - 150
VL  - 16
IS  - 1
PB  - Annales mathématiques Blaise Pascal
UR  - https://ambp.centre-mersenne.org/articles/10.5802/ambp.260/
DO  - 10.5802/ambp.260
LA  - fr
ID  - AMBP_2009__16_1_139_0
ER  - 
%0 Journal Article
%A Farid Kourki
%T Sur les Extensions Triviales Commutatives
%J Annales mathématiques Blaise Pascal
%D 2009
%P 139-150
%V 16
%N 1
%I Annales mathématiques Blaise Pascal
%U https://ambp.centre-mersenne.org/articles/10.5802/ambp.260/
%R 10.5802/ambp.260
%G fr
%F AMBP_2009__16_1_139_0

[1] N. Bourbaki Algèbre commutative, Chapitres 1 et 2, Masson, Paris, 1985

[2] C. Faith Annihilator ideals, associated primes and Kasch-McCoy commutative rings, Comm. Algebra, Volume 19 (1994), pp. 1867-1892 | Zbl | MR

[3] S. Glaz Commutative coherent rings, Lecture Notes in Math., Springer–Verlag, 1989 | Zbl | MR

[4] K.R. Goodearl Ring Theory : Nonsingular Rings and Modules, Marcel Dekker, New York, 1976 | Zbl | MR

[5] J.A. Huckaba Commutative rings with zero divisors, Marcel Dekker, NewYork-Basel, 1988 | Zbl | MR

[6] F. Kasch Modules and rings, Academic Press, London, 1982 (English translation) | Zbl | MR

[7] T.Y. Lam Lectures on modules and rings, Graduate Texts in Math., NewYork-Basel, 1999 | Zbl | MR

[8] W.K. Nicholson; M.F. Yousif Mininjective rings, J. Algebra, Volume 187 (1997), pp. 548-578 | DOI | Zbl | MR

[9] P. Vamos The dual of the notion of ’finitely generated’, J. London Math. Soc., Volume 43 (1968), pp. 643-646 | DOI | Zbl | MR

Cited by Sources: