On Commutative Trivial extensions

Farid Kourki[1]

  • [1] Département de Mathématiques et Informatique Université Abdelmalek Essaâdi Faculté des Sciences, B.P. 2121 Tétouan, Maroc

Annales mathématiques Blaise Pascal (2009)

  • Volume: 16, Issue: 1, page 139-150
  • ISSN: 1259-1734

Abstract

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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.

How to cite

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Kourki, Farid. "Sur les Extensions Triviales Commutatives." Annales mathématiques Blaise Pascal 16.1 (2009): 139-150. <http://eudml.org/doc/10566>.

@article{Kourki2009,
abstract = {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.},
affiliation = {Département de Mathématiques et Informatique Université Abdelmalek Essaâdi Faculté des Sciences, B.P. 2121 Tétouan, Maroc},
author = {Kourki, Farid},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Trivial extensions; SemiGoldie; Mininjective; Quasi-Frobenius},
language = {fre},
month = {1},
number = {1},
pages = {139-150},
publisher = {Annales mathématiques Blaise Pascal},
title = {Sur les Extensions Triviales Commutatives},
url = {http://eudml.org/doc/10566},
volume = {16},
year = {2009},
}

TY - JOUR
AU - Kourki, Farid
TI - Sur les Extensions Triviales Commutatives
JO - Annales mathématiques Blaise Pascal
DA - 2009/1//
PB - Annales mathématiques Blaise Pascal
VL - 16
IS - 1
SP - 139
EP - 150
AB - 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.
LA - fre
KW - Trivial extensions; SemiGoldie; Mininjective; Quasi-Frobenius
UR - http://eudml.org/doc/10566
ER -

References

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  4. K.R. Goodearl, Ring Theory : Nonsingular Rings and Modules, (1976), Marcel Dekker, New York Zbl0336.16001MR429962
  5. J.A. Huckaba, Commutative rings with zero divisors, (1988), Marcel Dekker, NewYork-Basel Zbl0637.13001MR938741
  6. F. Kasch, Modules and rings, (1982), Academic Press, London Zbl0523.16001MR667346
  7. T.Y. Lam, Lectures on modules and rings, (1999), Graduate Texts in Math., NewYork-Basel Zbl0911.16001MR1653294
  8. W.K. Nicholson, M.F. Yousif, Mininjective rings, J. Algebra 187 (1997), 548-578 Zbl0879.16002MR1430998
  9. P. Vamos, The dual of the notion of ’finitely generated’, J. London Math. Soc. 43 (1968), 643-646 Zbl0164.04003MR248171

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