Research Article
BibTex RIS Cite

GORENSTEIN $\pi[T]$-PROJECTIVITY WITH RESPECT TO A TILTING MODULE

Year 2020, Volume: 27 Issue: 27, 114 - 126, 07.01.2020
https://doi.org/10.24330/ieja.662993

Abstract

Let $T$ be a tilting module. In this paper, Gorenstein $\pi[T]$-projective modules are introduced and some of their basic properties are studied. Moreover, some characterizations of rings over which all modules are Gorenstein $\pi[T]$-projective are given. For instance, on the $T$-cocoherent rings, it is proved that the Gorenstein $\pi[T]$-projectivity of all $R$-modules is equivalent to the $\pi[T]$-projectivity of $\sigma[T]$-injective as a module.

References

  • M. Amini and F. Hasani, Copresented dimension of modules, Iran. J. Math. Sci. Inform., 14(2) (2019), 153-157.
  • F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Graduate Texts in Mathematics, 13, Springer-Verlag, New York-Heidelberg, 1974.
  • S. Bazzoni, A characterization of n-cotilting and n-tilting modules, J. Algebra, 273(1) (2004), 359-372.
  • E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, De Gruyter Expositions in Mathematics, 30, Walter de Gruyter & Co., Berlin, 2000.
  • S. Glaz, Commutative Coherent Rings, Lecture Notes in Mathematics, 1371, Springer-Verlag, Berlin, 1989.
  • M. J. Nikmehr and F. Shaveisi, Relative T-injective modules and relative T- flat modules, Chin. Ann. Math. Ser. B, 32(4) (2011), 497-506.
  • M. J. Nikmehr and F. Shaveisi, T-dimension and (n+ 1/2 ; T)-projective modules, Southeast Asian Bull. Math., 36 (2012), 113-123.
  • J. J. Rotman, An Introduction to Homological Algebra, Second edition, Uni- versitext, Springer, New York, 2009.
  • F. Shaveisi, M. Amini and M. H. Bijanzadeh, Gorenstein \sigma[T]-injectivity on T-coherent rings, Asian-Eur. J. Math., 8(4) (2015), 1550083 (9 pp).
  • R. Wisbauer, Foundations of Module and Ring Theory, Algebra, Logic and Applications, 3, Gordon and Breach Science Publishers, Philadelphia, PA, 1991.
  • W. Xue, On n-presented modules and almost excellent extensions, Comm. Al- gebra, 27(3) (1999), 1091-1102.
  • Z. M. Zhu and J. L. Chen, FCP-projective modules and some rings, J. Zhejiang Univ. Sci. Ed., 37(2) (2010), 126-130.
Year 2020, Volume: 27 Issue: 27, 114 - 126, 07.01.2020
https://doi.org/10.24330/ieja.662993

Abstract

References

  • M. Amini and F. Hasani, Copresented dimension of modules, Iran. J. Math. Sci. Inform., 14(2) (2019), 153-157.
  • F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Graduate Texts in Mathematics, 13, Springer-Verlag, New York-Heidelberg, 1974.
  • S. Bazzoni, A characterization of n-cotilting and n-tilting modules, J. Algebra, 273(1) (2004), 359-372.
  • E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, De Gruyter Expositions in Mathematics, 30, Walter de Gruyter & Co., Berlin, 2000.
  • S. Glaz, Commutative Coherent Rings, Lecture Notes in Mathematics, 1371, Springer-Verlag, Berlin, 1989.
  • M. J. Nikmehr and F. Shaveisi, Relative T-injective modules and relative T- flat modules, Chin. Ann. Math. Ser. B, 32(4) (2011), 497-506.
  • M. J. Nikmehr and F. Shaveisi, T-dimension and (n+ 1/2 ; T)-projective modules, Southeast Asian Bull. Math., 36 (2012), 113-123.
  • J. J. Rotman, An Introduction to Homological Algebra, Second edition, Uni- versitext, Springer, New York, 2009.
  • F. Shaveisi, M. Amini and M. H. Bijanzadeh, Gorenstein \sigma[T]-injectivity on T-coherent rings, Asian-Eur. J. Math., 8(4) (2015), 1550083 (9 pp).
  • R. Wisbauer, Foundations of Module and Ring Theory, Algebra, Logic and Applications, 3, Gordon and Breach Science Publishers, Philadelphia, PA, 1991.
  • W. Xue, On n-presented modules and almost excellent extensions, Comm. Al- gebra, 27(3) (1999), 1091-1102.
  • Z. M. Zhu and J. L. Chen, FCP-projective modules and some rings, J. Zhejiang Univ. Sci. Ed., 37(2) (2010), 126-130.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

M. Amini This is me

Publication Date January 7, 2020
Published in Issue Year 2020 Volume: 27 Issue: 27

Cite

APA Amini, M. (2020). GORENSTEIN $\pi[T]$-PROJECTIVITY WITH RESPECT TO A TILTING MODULE. International Electronic Journal of Algebra, 27(27), 114-126. https://doi.org/10.24330/ieja.662993
AMA Amini M. GORENSTEIN $\pi[T]$-PROJECTIVITY WITH RESPECT TO A TILTING MODULE. IEJA. January 2020;27(27):114-126. doi:10.24330/ieja.662993
Chicago Amini, M. “GORENSTEIN $\pi[T]$-PROJECTIVITY WITH RESPECT TO A TILTING MODULE”. International Electronic Journal of Algebra 27, no. 27 (January 2020): 114-26. https://doi.org/10.24330/ieja.662993.
EndNote Amini M (January 1, 2020) GORENSTEIN $\pi[T]$-PROJECTIVITY WITH RESPECT TO A TILTING MODULE. International Electronic Journal of Algebra 27 27 114–126.
IEEE M. Amini, “GORENSTEIN $\pi[T]$-PROJECTIVITY WITH RESPECT TO A TILTING MODULE”, IEJA, vol. 27, no. 27, pp. 114–126, 2020, doi: 10.24330/ieja.662993.
ISNAD Amini, M. “GORENSTEIN $\pi[T]$-PROJECTIVITY WITH RESPECT TO A TILTING MODULE”. International Electronic Journal of Algebra 27/27 (January 2020), 114-126. https://doi.org/10.24330/ieja.662993.
JAMA Amini M. GORENSTEIN $\pi[T]$-PROJECTIVITY WITH RESPECT TO A TILTING MODULE. IEJA. 2020;27:114–126.
MLA Amini, M. “GORENSTEIN $\pi[T]$-PROJECTIVITY WITH RESPECT TO A TILTING MODULE”. International Electronic Journal of Algebra, vol. 27, no. 27, 2020, pp. 114-26, doi:10.24330/ieja.662993.
Vancouver Amini M. GORENSTEIN $\pi[T]$-PROJECTIVITY WITH RESPECT TO A TILTING MODULE. IEJA. 2020;27(27):114-26.