Araştırma Makalesi
Yıl 2020,
Cilt: 27 Sayı: 27, 114 - 126, 07.01.2020
Öz
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.
Anahtar Kelimeler
Kaynakça
- 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.
Yıl 2020,
Cilt: 27 Sayı: 27, 114 - 126, 07.01.2020
Öz
Kaynakça
- 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.
Toplam 12 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 7 Ocak 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 27 Sayı: 27 |