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Year 2021, Volume: 9 Issue: 1, 100 - 101, 28.04.2021

Abstract

References

  • [1] Adamek, J. and Rosicky, J., Locally presentable and accessible categories, Cambridge University Press, Cambridge, 1994.
  • [2] Berktas¸, M. K., On pure Goldie dimensions, Comm. Algebra 45 (2017), 3334-3339.
  • [3] Crivei, S. and Radu S. M., CS-Rickart and dual CS-Rickart objects in abelian categories, arxiv: 2007.11059v1
  • [4] Crawley-Boevey, W., Locally finitely presented additive categories, Comm. Algebra 22 (1994), 1641-1674.
  • [5] Dehghani, N. and Rizvi, S. T., When mutually subisomorphic Baer modules are isomorphic, arxiv: 1909.0344v1
  • [6] Dung, N. V., Huynh, D. V., Smith, P. F. and Wisbauer, R., Extending modules, Longman, 1994.
  • [7] Herzog, I., Pure injective envelopes, J. Algebra Appl. 4 (2003), 397–402.
  • [8] Rizvi, S. T. and Roman, C. S., On K -nonsingular modules and applications, Comm. Algebra 35 (2007), 2960–2982.

Pure Extending Objects

Year 2021, Volume: 9 Issue: 1, 100 - 101, 28.04.2021

Abstract

In this paper we introduce two new concepts, namely, pure extending objects and $\mathcal{K}$-nonsingular objects and then, we prove that any pair of subisomorphic $\mathcal{K}$-nonsingular objects in a finitely accessible additive category with kernels $\mathcal{A}$ are isomorphic to each other if and only if for any object $Y$ and any pure extending $\mathcal{K}$-nonsingular object $X$, if $X$ and $Y$ are subisomorphic to each other then $X\cong Y$.

References

  • [1] Adamek, J. and Rosicky, J., Locally presentable and accessible categories, Cambridge University Press, Cambridge, 1994.
  • [2] Berktas¸, M. K., On pure Goldie dimensions, Comm. Algebra 45 (2017), 3334-3339.
  • [3] Crivei, S. and Radu S. M., CS-Rickart and dual CS-Rickart objects in abelian categories, arxiv: 2007.11059v1
  • [4] Crawley-Boevey, W., Locally finitely presented additive categories, Comm. Algebra 22 (1994), 1641-1674.
  • [5] Dehghani, N. and Rizvi, S. T., When mutually subisomorphic Baer modules are isomorphic, arxiv: 1909.0344v1
  • [6] Dung, N. V., Huynh, D. V., Smith, P. F. and Wisbauer, R., Extending modules, Longman, 1994.
  • [7] Herzog, I., Pure injective envelopes, J. Algebra Appl. 4 (2003), 397–402.
  • [8] Rizvi, S. T. and Roman, C. S., On K -nonsingular modules and applications, Comm. Algebra 35 (2007), 2960–2982.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Mustafa Kemal Berktaş 0000-0003-4395-9521

Publication Date April 28, 2021
Submission Date January 11, 2021
Acceptance Date February 11, 2021
Published in Issue Year 2021 Volume: 9 Issue: 1

Cite

APA Berktaş, M. K. (2021). Pure Extending Objects. Konuralp Journal of Mathematics, 9(1), 100-101.
AMA Berktaş MK. Pure Extending Objects. Konuralp J. Math. April 2021;9(1):100-101.
Chicago Berktaş, Mustafa Kemal. “Pure Extending Objects”. Konuralp Journal of Mathematics 9, no. 1 (April 2021): 100-101.
EndNote Berktaş MK (April 1, 2021) Pure Extending Objects. Konuralp Journal of Mathematics 9 1 100–101.
IEEE M. K. Berktaş, “Pure Extending Objects”, Konuralp J. Math., vol. 9, no. 1, pp. 100–101, 2021.
ISNAD Berktaş, Mustafa Kemal. “Pure Extending Objects”. Konuralp Journal of Mathematics 9/1 (April 2021), 100-101.
JAMA Berktaş MK. Pure Extending Objects. Konuralp J. Math. 2021;9:100–101.
MLA Berktaş, Mustafa Kemal. “Pure Extending Objects”. Konuralp Journal of Mathematics, vol. 9, no. 1, 2021, pp. 100-1.
Vancouver Berktaş MK. Pure Extending Objects. Konuralp J. Math. 2021;9(1):100-1.
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