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ON CLASSES OF MODULES CLOSED UNDER INJECTIVE HULLS AND ARTINIAN PRINCIPAL IDEAL RINGS

Year 2014, , 1 - 12, 01.06.2014
https://doi.org/10.24330/ieja.266233

Abstract

In this work we consider some classes of modules closed under
certain closure properties such as being closed under taking submodules, quotients,
injective hulls and direct sums. We obtain some characterizations of
artinian principal ideal rings using properties of big lattices of module classes.

References

  • A. Alvarado, H. Rinc´on and J. R´ıos, On some lattices of module classes, J. Algebra Appl., 5(1) (2006), 105-117.
  • F. Anderson and K. Fuller, Rings and Categories of Modules, Springer-Verlag, New York, 1992.
  • A. Boyle, When projective covers and injective hulls are isomorphic, Bull. Aus- tral. Math. Soc., 8 (1973), 471-476.
  • R. Bronowitz and M. L. Teply, Torsion theories of simple type, J. Pure Appl. Algebra, 3 (1973), 329-336.
  • A. El Mejdani, H. Essannouni and A. Kaidi, Rings with nice Artinian Modules, Int. J. Algebra, 18(2) (2008), 895-904.
  • C. Faith, On K¨othe rings, Math. Ann., 164 (1966), 207-212.
  • C. Faith, Algebra II, Ring Theory, Grundlehren der mathematischen Wis- senschaften 191, Springer-Verlag, 1976.
  • F. Kasch, Modules and rings, Academic Press, London, 1982.
  • T. Y. Lam, Lectures on Modules and Rings, Springer- Verlag, New York, 1999.
  • A. Rosenberg and D. Zelinsky, Finiteness of the injective hull, Math. Z., 70 (1959), 372-378.
  • R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach Science Publishers, 1991.
  • Alejandro Alvarado-Garc´ıa, C´esar Cejudo-Castilla, Hugo Alberto Rinc´on-Mej´ıa, Ivan Fernando Vilchis-Montalvo Departmento de Matem´aticas Facultad de Ciencias Universidad Nacional Aut´onoma de M´exico Circuito Exterior, C.U. M´exico, D.F. e-mails: alejandroalvaradogarcia@gmail.com (A. Alvarado G.) cesarcc@ciencias.unam.mx (C. Cejudo C.) hurincon@gmail.com (H. A. Rinc´on M.) vilchis.f@gmail.com (I.F. Vilchis M.)
Year 2014, , 1 - 12, 01.06.2014
https://doi.org/10.24330/ieja.266233

Abstract

References

  • A. Alvarado, H. Rinc´on and J. R´ıos, On some lattices of module classes, J. Algebra Appl., 5(1) (2006), 105-117.
  • F. Anderson and K. Fuller, Rings and Categories of Modules, Springer-Verlag, New York, 1992.
  • A. Boyle, When projective covers and injective hulls are isomorphic, Bull. Aus- tral. Math. Soc., 8 (1973), 471-476.
  • R. Bronowitz and M. L. Teply, Torsion theories of simple type, J. Pure Appl. Algebra, 3 (1973), 329-336.
  • A. El Mejdani, H. Essannouni and A. Kaidi, Rings with nice Artinian Modules, Int. J. Algebra, 18(2) (2008), 895-904.
  • C. Faith, On K¨othe rings, Math. Ann., 164 (1966), 207-212.
  • C. Faith, Algebra II, Ring Theory, Grundlehren der mathematischen Wis- senschaften 191, Springer-Verlag, 1976.
  • F. Kasch, Modules and rings, Academic Press, London, 1982.
  • T. Y. Lam, Lectures on Modules and Rings, Springer- Verlag, New York, 1999.
  • A. Rosenberg and D. Zelinsky, Finiteness of the injective hull, Math. Z., 70 (1959), 372-378.
  • R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach Science Publishers, 1991.
  • Alejandro Alvarado-Garc´ıa, C´esar Cejudo-Castilla, Hugo Alberto Rinc´on-Mej´ıa, Ivan Fernando Vilchis-Montalvo Departmento de Matem´aticas Facultad de Ciencias Universidad Nacional Aut´onoma de M´exico Circuito Exterior, C.U. M´exico, D.F. e-mails: alejandroalvaradogarcia@gmail.com (A. Alvarado G.) cesarcc@ciencias.unam.mx (C. Cejudo C.) hurincon@gmail.com (H. A. Rinc´on M.) vilchis.f@gmail.com (I.F. Vilchis M.)
There are 12 citations in total.

Details

Other ID JA76BB53RD
Journal Section Articles
Authors

Alejandro Alvarado-garcía This is me

César Cejudo-castilla This is me

Hugo Alberto Rincón-mejía This is me

Ivan Fernando Vilchis-montalvo This is me

Publication Date June 1, 2014
Published in Issue Year 2014

Cite

APA Alvarado-garcía, A., Cejudo-castilla, C., Rincón-mejía, H. A., Vilchis-montalvo, I. F. (2014). ON CLASSES OF MODULES CLOSED UNDER INJECTIVE HULLS AND ARTINIAN PRINCIPAL IDEAL RINGS. International Electronic Journal of Algebra, 15(15), 1-12. https://doi.org/10.24330/ieja.266233
AMA Alvarado-garcía A, Cejudo-castilla C, Rincón-mejía HA, Vilchis-montalvo IF. ON CLASSES OF MODULES CLOSED UNDER INJECTIVE HULLS AND ARTINIAN PRINCIPAL IDEAL RINGS. IEJA. June 2014;15(15):1-12. doi:10.24330/ieja.266233
Chicago Alvarado-garcía, Alejandro, César Cejudo-castilla, Hugo Alberto Rincón-mejía, and Ivan Fernando Vilchis-montalvo. “ON CLASSES OF MODULES CLOSED UNDER INJECTIVE HULLS AND ARTINIAN PRINCIPAL IDEAL RINGS”. International Electronic Journal of Algebra 15, no. 15 (June 2014): 1-12. https://doi.org/10.24330/ieja.266233.
EndNote Alvarado-garcía A, Cejudo-castilla C, Rincón-mejía HA, Vilchis-montalvo IF (June 1, 2014) ON CLASSES OF MODULES CLOSED UNDER INJECTIVE HULLS AND ARTINIAN PRINCIPAL IDEAL RINGS. International Electronic Journal of Algebra 15 15 1–12.
IEEE A. Alvarado-garcía, C. Cejudo-castilla, H. A. Rincón-mejía, and I. F. Vilchis-montalvo, “ON CLASSES OF MODULES CLOSED UNDER INJECTIVE HULLS AND ARTINIAN PRINCIPAL IDEAL RINGS”, IEJA, vol. 15, no. 15, pp. 1–12, 2014, doi: 10.24330/ieja.266233.
ISNAD Alvarado-garcía, Alejandro et al. “ON CLASSES OF MODULES CLOSED UNDER INJECTIVE HULLS AND ARTINIAN PRINCIPAL IDEAL RINGS”. International Electronic Journal of Algebra 15/15 (June 2014), 1-12. https://doi.org/10.24330/ieja.266233.
JAMA Alvarado-garcía A, Cejudo-castilla C, Rincón-mejía HA, Vilchis-montalvo IF. ON CLASSES OF MODULES CLOSED UNDER INJECTIVE HULLS AND ARTINIAN PRINCIPAL IDEAL RINGS. IEJA. 2014;15:1–12.
MLA Alvarado-garcía, Alejandro et al. “ON CLASSES OF MODULES CLOSED UNDER INJECTIVE HULLS AND ARTINIAN PRINCIPAL IDEAL RINGS”. International Electronic Journal of Algebra, vol. 15, no. 15, 2014, pp. 1-12, doi:10.24330/ieja.266233.
Vancouver Alvarado-garcía A, Cejudo-castilla C, Rincón-mejía HA, Vilchis-montalvo IF. ON CLASSES OF MODULES CLOSED UNDER INJECTIVE HULLS AND ARTINIAN PRINCIPAL IDEAL RINGS. IEJA. 2014;15(15):1-12.

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