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Year 2021, Volume: 70 Issue: 1, 265 - 268, 30.06.2021
https://doi.org/10.31801/cfsuasmas.733614

Abstract

References

  • Adámek, J. and Rosicky, J., Locally presentable and accessible categories, Cambridge University Press, Cambridge, 1994.
  • Alahmadi, A., Facchini, A. and Tung, N. K., Automorphism-invariant modules, Rend. Semin. Mat Univ. Padova, 133 (2015), 241--259.
  • Berktaş, M. K., A uniqueness theorem in a finitely accessible additive category, Algebr. Represent. Theor., 17 (2014), 1009--1012.
  • Berktaş, M. K., On objects with a semilocal endomorphism rings in finitely accessible additive categories, Algebr. Represent. Theor., 18 (2015), 1389--1393.
  • Berktaş, M. K., On pure Goldie dimensions, Comm. Algebra, 45 (2017), 3334--3339.
  • Berktaş, M. K. and Keskin Tütüncü, D., The Schröder-Bernstein problem for objects in Grothendieck categories, preprint.
  • Crawley-Boevey, W., Locally finitely presented additive categories, Comm. Algebra, 22 (1994), 1641--1674.
  • Er, N., Singh, S. and Srivastava, A. K., Rings and modules which are stable under automorphisms of their injective hulls, J. Algebra, 379 (2013), 223--229.
  • Facchini, A. and Herbera, D., Local morphisms and modules with a semilocal endomorphism ring, Algebr. Represent. Theor., 9 (2006), 403--422.
  • Guil Asensio, P. A., Kalebogaz, B. and Srivastava A. K., The Schröder-Bernstein problem for modules, J. Algebra 498 (2018), 153-164.
  • Krause, H. Uniqueness of uniform decompositions in abelian categories, J. Pure Appl. Algebra, 183 (2003), 125--128.

Pseudo pure-injective objects

Year 2021, Volume: 70 Issue: 1, 265 - 268, 30.06.2021
https://doi.org/10.31801/cfsuasmas.733614

Abstract

We show that if M and N are pure essentially equivalent objects in a finitely accessible additive category A such that M is pseudo pure-N- injective and N is pseudo pure-M-injective, then M≅N.

References

  • Adámek, J. and Rosicky, J., Locally presentable and accessible categories, Cambridge University Press, Cambridge, 1994.
  • Alahmadi, A., Facchini, A. and Tung, N. K., Automorphism-invariant modules, Rend. Semin. Mat Univ. Padova, 133 (2015), 241--259.
  • Berktaş, M. K., A uniqueness theorem in a finitely accessible additive category, Algebr. Represent. Theor., 17 (2014), 1009--1012.
  • Berktaş, M. K., On objects with a semilocal endomorphism rings in finitely accessible additive categories, Algebr. Represent. Theor., 18 (2015), 1389--1393.
  • Berktaş, M. K., On pure Goldie dimensions, Comm. Algebra, 45 (2017), 3334--3339.
  • Berktaş, M. K. and Keskin Tütüncü, D., The Schröder-Bernstein problem for objects in Grothendieck categories, preprint.
  • Crawley-Boevey, W., Locally finitely presented additive categories, Comm. Algebra, 22 (1994), 1641--1674.
  • Er, N., Singh, S. and Srivastava, A. K., Rings and modules which are stable under automorphisms of their injective hulls, J. Algebra, 379 (2013), 223--229.
  • Facchini, A. and Herbera, D., Local morphisms and modules with a semilocal endomorphism ring, Algebr. Represent. Theor., 9 (2006), 403--422.
  • Guil Asensio, P. A., Kalebogaz, B. and Srivastava A. K., The Schröder-Bernstein problem for modules, J. Algebra 498 (2018), 153-164.
  • Krause, H. Uniqueness of uniform decompositions in abelian categories, J. Pure Appl. Algebra, 183 (2003), 125--128.
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Mustafa Kemal Berktaş 0000-0003-4395-9521

Publication Date June 30, 2021
Submission Date May 7, 2020
Acceptance Date December 19, 2020
Published in Issue Year 2021 Volume: 70 Issue: 1

Cite

APA Berktaş, M. K. (2021). Pseudo pure-injective objects. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(1), 265-268. https://doi.org/10.31801/cfsuasmas.733614
AMA Berktaş MK. Pseudo pure-injective objects. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2021;70(1):265-268. doi:10.31801/cfsuasmas.733614
Chicago Berktaş, Mustafa Kemal. “Pseudo Pure-Injective Objects”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 1 (June 2021): 265-68. https://doi.org/10.31801/cfsuasmas.733614.
EndNote Berktaş MK (June 1, 2021) Pseudo pure-injective objects. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 1 265–268.
IEEE M. K. Berktaş, “Pseudo pure-injective objects”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 1, pp. 265–268, 2021, doi: 10.31801/cfsuasmas.733614.
ISNAD Berktaş, Mustafa Kemal. “Pseudo Pure-Injective Objects”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/1 (June 2021), 265-268. https://doi.org/10.31801/cfsuasmas.733614.
JAMA Berktaş MK. Pseudo pure-injective objects. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:265–268.
MLA Berktaş, Mustafa Kemal. “Pseudo Pure-Injective Objects”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 1, 2021, pp. 265-8, doi:10.31801/cfsuasmas.733614.
Vancouver Berktaş MK. Pseudo pure-injective objects. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(1):265-8.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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