Araştırma Makalesi
BibTex RIS Kaynak Göster

$(n,d)$-$\mathcal{X}_R$-phantom and $(n,d)$-$_R\mathcal{X}$-cophantom morphisms

Yıl 2023, Cilt: 34 Sayı: 34, 210 - 236, 10.07.2023
https://doi.org/10.24330/ieja.1260503

Öz

Several authors have been interested in some like phantom
morphisms such as $d$-phantoms,
$d$-$\operatorname{Ext}$-phantoms, neat-phantom morphisms, clean-
cophantom morphisms, $RD$-phantom morphisms and
$RD$-$\operatorname{Ext}$-phantom morphisms. In this paper, we
prove that these notions can be unified. We are mainly interested
in proving that the majority of the existing results hold true in
our general framework.

Kaynakça

  • M. Auslander and O. Solberg, Relative homology and representation theory I, relative homology and homologically finite categories, Comm. Algebra, 21(9) (1993), 2995-3031.
  • D. Bennis, $n$-$\mathcal{X}$-coherent rings, Int. Electron. J. Algebra, 7 (2010), 128-139.
  • J. Chen and N. Ding, On $n$-coherent rings, Comm. Algebra, 24(10) (1996), 3211-216.
  • S. Crivei, M. Prest and B. Torrecillas, Covers in finitely accessible categories, Proc. Amer. Math. Soc., 138(4) (2010), 1213-1221.
  • X. H. Fu, P. A. Guil Asensio, I. Herzog and B. Torrecillas, Ideal approximation theory, Adv. Math., 244 (2013), 750-790.
  • I. Herzog, The phantom cover of a module, Adv. Math., 215 (2007), 220-249.
  • I. Herzog, Contravariant functors on the category of finitely presented modules, Israel J. Math., 167 (2008), 347-410.
  • K. Lan and B. Lu, On $n$-phantom and $n$-Ext-phantom morphisms, Taiwanese J. Math., 25 (2021), 941-957.
  • L. X. Mao, On covers and envelopes in some functor categories, Comm. Algebra, 41(5) (2013), 1655-1684.
  • L. X. Mao, Precovers and preenvelopes by phantom and Ext-phantom morphisms, Comm. Algebra, 44(4) (2016), 1704-1721.
  • L. X. Mao, RD-phantom and RD-Ext-phantom morphisms, Filomat, 32(8) (2018), 2883-2895.
  • L. X. Mao, Higher phantom and Ext-phantom morphisms, J. Algebra Appl., 17(1) (2018), 1850012 (15 pp).
  • L. X. Mao, Higher phantom morphisms with respect to a subfunctor of Ext, Algebr. Represent. Theory, 22(2) (2019), 407-424.
  • L. X. Mao, Neat-phantom and clean-cophantom morphisms, J. Algebra Appl., 20(9) (2021), 2150172 (24 pp).
  • L. X. Mao and N. Q. Ding, Envelopes and covers by modules of finite FP-injective and flat dimensions, Comm. Algebra, 35(3) (2007), 833-849.
  • C. A. McGibbon, Phantom maps, in Handboook of Algebraic Topology, North-Holland, Amsterdam, (1995), 1209-1257.
  • J. J. Rotman, An Introduction to Homological Algebra, Pure and Applied Mathematics, 85, Academic Press, Inc., New York-London, 1979.
Yıl 2023, Cilt: 34 Sayı: 34, 210 - 236, 10.07.2023
https://doi.org/10.24330/ieja.1260503

Öz

Kaynakça

  • M. Auslander and O. Solberg, Relative homology and representation theory I, relative homology and homologically finite categories, Comm. Algebra, 21(9) (1993), 2995-3031.
  • D. Bennis, $n$-$\mathcal{X}$-coherent rings, Int. Electron. J. Algebra, 7 (2010), 128-139.
  • J. Chen and N. Ding, On $n$-coherent rings, Comm. Algebra, 24(10) (1996), 3211-216.
  • S. Crivei, M. Prest and B. Torrecillas, Covers in finitely accessible categories, Proc. Amer. Math. Soc., 138(4) (2010), 1213-1221.
  • X. H. Fu, P. A. Guil Asensio, I. Herzog and B. Torrecillas, Ideal approximation theory, Adv. Math., 244 (2013), 750-790.
  • I. Herzog, The phantom cover of a module, Adv. Math., 215 (2007), 220-249.
  • I. Herzog, Contravariant functors on the category of finitely presented modules, Israel J. Math., 167 (2008), 347-410.
  • K. Lan and B. Lu, On $n$-phantom and $n$-Ext-phantom morphisms, Taiwanese J. Math., 25 (2021), 941-957.
  • L. X. Mao, On covers and envelopes in some functor categories, Comm. Algebra, 41(5) (2013), 1655-1684.
  • L. X. Mao, Precovers and preenvelopes by phantom and Ext-phantom morphisms, Comm. Algebra, 44(4) (2016), 1704-1721.
  • L. X. Mao, RD-phantom and RD-Ext-phantom morphisms, Filomat, 32(8) (2018), 2883-2895.
  • L. X. Mao, Higher phantom and Ext-phantom morphisms, J. Algebra Appl., 17(1) (2018), 1850012 (15 pp).
  • L. X. Mao, Higher phantom morphisms with respect to a subfunctor of Ext, Algebr. Represent. Theory, 22(2) (2019), 407-424.
  • L. X. Mao, Neat-phantom and clean-cophantom morphisms, J. Algebra Appl., 20(9) (2021), 2150172 (24 pp).
  • L. X. Mao and N. Q. Ding, Envelopes and covers by modules of finite FP-injective and flat dimensions, Comm. Algebra, 35(3) (2007), 833-849.
  • C. A. McGibbon, Phantom maps, in Handboook of Algebraic Topology, North-Holland, Amsterdam, (1995), 1209-1257.
  • J. J. Rotman, An Introduction to Homological Algebra, Pure and Applied Mathematics, 85, Academic Press, Inc., New York-London, 1979.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Mourad Khattarı Bu kişi benim

Driss Bennıs Bu kişi benim

Erken Görünüm Tarihi 11 Mayıs 2023
Yayımlanma Tarihi 10 Temmuz 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 34 Sayı: 34

Kaynak Göster

APA Khattarı, M., & Bennıs, D. (2023). $(n,d)$-$\mathcal{X}_R$-phantom and $(n,d)$-$_R\mathcal{X}$-cophantom morphisms. International Electronic Journal of Algebra, 34(34), 210-236. https://doi.org/10.24330/ieja.1260503
AMA Khattarı M, Bennıs D. $(n,d)$-$\mathcal{X}_R$-phantom and $(n,d)$-$_R\mathcal{X}$-cophantom morphisms. IEJA. Temmuz 2023;34(34):210-236. doi:10.24330/ieja.1260503
Chicago Khattarı, Mourad, ve Driss Bennıs. “$(n,d)$-$\mathcal{X}_R$-Phantom and $(n,d)$-$_R\mathcal{X}$-Cophantom Morphisms”. International Electronic Journal of Algebra 34, sy. 34 (Temmuz 2023): 210-36. https://doi.org/10.24330/ieja.1260503.
EndNote Khattarı M, Bennıs D (01 Temmuz 2023) $(n,d)$-$\mathcal{X}_R$-phantom and $(n,d)$-$_R\mathcal{X}$-cophantom morphisms. International Electronic Journal of Algebra 34 34 210–236.
IEEE M. Khattarı ve D. Bennıs, “$(n,d)$-$\mathcal{X}_R$-phantom and $(n,d)$-$_R\mathcal{X}$-cophantom morphisms”, IEJA, c. 34, sy. 34, ss. 210–236, 2023, doi: 10.24330/ieja.1260503.
ISNAD Khattarı, Mourad - Bennıs, Driss. “$(n,d)$-$\mathcal{X}_R$-Phantom and $(n,d)$-$_R\mathcal{X}$-Cophantom Morphisms”. International Electronic Journal of Algebra 34/34 (Temmuz 2023), 210-236. https://doi.org/10.24330/ieja.1260503.
JAMA Khattarı M, Bennıs D. $(n,d)$-$\mathcal{X}_R$-phantom and $(n,d)$-$_R\mathcal{X}$-cophantom morphisms. IEJA. 2023;34:210–236.
MLA Khattarı, Mourad ve Driss Bennıs. “$(n,d)$-$\mathcal{X}_R$-Phantom and $(n,d)$-$_R\mathcal{X}$-Cophantom Morphisms”. International Electronic Journal of Algebra, c. 34, sy. 34, 2023, ss. 210-36, doi:10.24330/ieja.1260503.
Vancouver Khattarı M, Bennıs D. $(n,d)$-$\mathcal{X}_R$-phantom and $(n,d)$-$_R\mathcal{X}$-cophantom morphisms. IEJA. 2023;34(34):210-36.