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ON CONATURAL CLASSES AND COTYPE SUBMODULES

Year 2012, Volume: 11 Issue: 11, 64 - 81, 01.06.2012

Abstract

The concepts of cotype submodule and cotype dimension of a module are introduced, their basic properties are studied, and a characterization of the amply supplemented modules with finite cotype dimension is given.

References

  • A. Alvarado-Garc´ıa, H. A. Rinc´on-Mej´ıa and J. R´ıos-Montes, On the lattices of natural and conatural classes in R-mod, Comm. Algebra, 29(2) (2001), 541
  • A. Alvarado-Garc´ıa, H. A. Rinc´on-Mej´ıa and J. R´ıos-Montes, On some lattices of module classes, J. Algebra Appl., 5(1) (2006), 105-117.
  • F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Second Edition, Springer-Verlag, 1992.
  • J. Clark, C. Lomp, N. Vanaja, and R. Wisbauer, Lifting Modules. Supplements and Projectivity in Module Theory, Frontiers in Mathematics, Birkh¨auser Ver- lag, Basel, 2006.
  • I. Crivei and S. Crivei, Associated classes of modules, Stud. Univ. Babe¸s-Bolyai Math., 54(2) (2009), 23-32.
  • S. Crivei and B. Torrecillas, On some monic covers and epic envelopes, Arab. J. Sci. Eng. Sect. C, 33(2) (2008), 123-135.
  • J. Dauns and Y. Zhou, Classes of Modules, Pure and Applied Mathematics (Boca Raton), 281. Chapman & Hall/CRC, Boca Raton, FL, 2006.
  • F. Kasch, Modules and Rings, Academic Press Inc. (London) Ltd, 1982.
  • A. I. Kashu, On natural classes of R-modules in the language of ring R, Bul. Acad. S¸tiinte Repub. Mold. Mat., 2(45) (2004), 95-101.
  • A. I. Kashu, On the lattice of closed classes of modules, Bul. Acad. S¸tiinte Repub. Mold. Mat., 2(48) (2005), 43-50.
  • A. I. Kashu, Natural classes and torsion free classes in categories of modules, Bul. Acad. S¸tiinte Repub. Mold. Mat., 3(52) (2006), 101-108.
  • A. I. Kashu, On natural and conatural sets of left ideals of a ring, Bul. Acad. S¸tiinte Repub. Mold. Mat., 2(54) (2007), 25-32.
  • D. Keskin, On lifting modules, Comm. Algebra, 28 (2000), 3427-3440.
  • R. Wisbauer, Foundations of Module and Ring Theory: A handbook for study and research, Gordon and Breach Science Publishers, 1991.
  • Y. Zhou, Decomposing modules into direct sums of submodules with types, J. Pure Appl. Algebra, 138 (1999), 83-97.
  • Alejandro Alvarado-Garc´ıa, Hugo Alberto Rinc´on-Mej´ıa, Bertha Tom´e-Arreola 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) hurincon@gmail.com (H. Rinc´on) bta@hp.fciencias.unam.mx (B. Tom´e) Jos´e R´ıos-Montes Instituto de Matem´aticas Universidad Nacional Aut´onoma de M´exico ´ Area de la Investigaci´on Cient´ıfica Circuito Exterior, C.U. M´exico D.F. e-mail: jrios@matem.unam.mx
Year 2012, Volume: 11 Issue: 11, 64 - 81, 01.06.2012

Abstract

References

  • A. Alvarado-Garc´ıa, H. A. Rinc´on-Mej´ıa and J. R´ıos-Montes, On the lattices of natural and conatural classes in R-mod, Comm. Algebra, 29(2) (2001), 541
  • A. Alvarado-Garc´ıa, H. A. Rinc´on-Mej´ıa and J. R´ıos-Montes, On some lattices of module classes, J. Algebra Appl., 5(1) (2006), 105-117.
  • F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Second Edition, Springer-Verlag, 1992.
  • J. Clark, C. Lomp, N. Vanaja, and R. Wisbauer, Lifting Modules. Supplements and Projectivity in Module Theory, Frontiers in Mathematics, Birkh¨auser Ver- lag, Basel, 2006.
  • I. Crivei and S. Crivei, Associated classes of modules, Stud. Univ. Babe¸s-Bolyai Math., 54(2) (2009), 23-32.
  • S. Crivei and B. Torrecillas, On some monic covers and epic envelopes, Arab. J. Sci. Eng. Sect. C, 33(2) (2008), 123-135.
  • J. Dauns and Y. Zhou, Classes of Modules, Pure and Applied Mathematics (Boca Raton), 281. Chapman & Hall/CRC, Boca Raton, FL, 2006.
  • F. Kasch, Modules and Rings, Academic Press Inc. (London) Ltd, 1982.
  • A. I. Kashu, On natural classes of R-modules in the language of ring R, Bul. Acad. S¸tiinte Repub. Mold. Mat., 2(45) (2004), 95-101.
  • A. I. Kashu, On the lattice of closed classes of modules, Bul. Acad. S¸tiinte Repub. Mold. Mat., 2(48) (2005), 43-50.
  • A. I. Kashu, Natural classes and torsion free classes in categories of modules, Bul. Acad. S¸tiinte Repub. Mold. Mat., 3(52) (2006), 101-108.
  • A. I. Kashu, On natural and conatural sets of left ideals of a ring, Bul. Acad. S¸tiinte Repub. Mold. Mat., 2(54) (2007), 25-32.
  • D. Keskin, On lifting modules, Comm. Algebra, 28 (2000), 3427-3440.
  • R. Wisbauer, Foundations of Module and Ring Theory: A handbook for study and research, Gordon and Breach Science Publishers, 1991.
  • Y. Zhou, Decomposing modules into direct sums of submodules with types, J. Pure Appl. Algebra, 138 (1999), 83-97.
  • Alejandro Alvarado-Garc´ıa, Hugo Alberto Rinc´on-Mej´ıa, Bertha Tom´e-Arreola 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) hurincon@gmail.com (H. Rinc´on) bta@hp.fciencias.unam.mx (B. Tom´e) Jos´e R´ıos-Montes Instituto de Matem´aticas Universidad Nacional Aut´onoma de M´exico ´ Area de la Investigaci´on Cient´ıfica Circuito Exterior, C.U. M´exico D.F. e-mail: jrios@matem.unam.mx
There are 16 citations in total.

Details

Other ID JA99DH57JZ
Journal Section Articles
Authors

Alejandro Alvarado-garcía This is me

Hugo Alberto Rincón-mejía This is me

José Ríos-montes This is me

Bertha Tomé-arreola This is me

Publication Date June 1, 2012
Published in Issue Year 2012 Volume: 11 Issue: 11

Cite

APA Alvarado-garcía, A., Rincón-mejía, H. A., Ríos-montes, J., Tomé-arreola, B. (2012). ON CONATURAL CLASSES AND COTYPE SUBMODULES. International Electronic Journal of Algebra, 11(11), 64-81.
AMA Alvarado-garcía A, Rincón-mejía HA, Ríos-montes J, Tomé-arreola B. ON CONATURAL CLASSES AND COTYPE SUBMODULES. IEJA. June 2012;11(11):64-81.
Chicago Alvarado-garcía, Alejandro, Hugo Alberto Rincón-mejía, José Ríos-montes, and Bertha Tomé-arreola. “ON CONATURAL CLASSES AND COTYPE SUBMODULES”. International Electronic Journal of Algebra 11, no. 11 (June 2012): 64-81.
EndNote Alvarado-garcía A, Rincón-mejía HA, Ríos-montes J, Tomé-arreola B (June 1, 2012) ON CONATURAL CLASSES AND COTYPE SUBMODULES. International Electronic Journal of Algebra 11 11 64–81.
IEEE A. Alvarado-garcía, H. A. Rincón-mejía, J. Ríos-montes, and B. Tomé-arreola, “ON CONATURAL CLASSES AND COTYPE SUBMODULES”, IEJA, vol. 11, no. 11, pp. 64–81, 2012.
ISNAD Alvarado-garcía, Alejandro et al. “ON CONATURAL CLASSES AND COTYPE SUBMODULES”. International Electronic Journal of Algebra 11/11 (June 2012), 64-81.
JAMA Alvarado-garcía A, Rincón-mejía HA, Ríos-montes J, Tomé-arreola B. ON CONATURAL CLASSES AND COTYPE SUBMODULES. IEJA. 2012;11:64–81.
MLA Alvarado-garcía, Alejandro et al. “ON CONATURAL CLASSES AND COTYPE SUBMODULES”. International Electronic Journal of Algebra, vol. 11, no. 11, 2012, pp. 64-81.
Vancouver Alvarado-garcía A, Rincón-mejía HA, Ríos-montes J, Tomé-arreola B. ON CONATURAL CLASSES AND COTYPE SUBMODULES. IEJA. 2012;11(11):64-81.