TY - JOUR T1 - Pure Extending Objects AU - Berktaş, Mustafa Kemal PY - 2021 DA - April Y2 - 2021 JF - Konuralp Journal of Mathematics JO - Konuralp J. Math. PB - Mehmet Zeki SARIKAYA WT - DergiPark SN - 2147-625X SP - 100 EP - 101 VL - 9 IS - 1 LA - en AB - 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 $X\cong Y$. KW - Finitely accessible category KW - Pure essential monomorphism KW - Nonsinguler object CR - [1] Adamek, J. and Rosicky, J., Locally presentable and accessible categories, Cambridge University Press, Cambridge, 1994. CR - [2] Berktas¸, M. K., On pure Goldie dimensions, Comm. Algebra 45 (2017), 3334-3339. CR - [3] Crivei, S. and Radu S. M., CS-Rickart and dual CS-Rickart objects in abelian categories, arxiv: 2007.11059v1 CR - [4] Crawley-Boevey, W., Locally finitely presented additive categories, Comm. Algebra 22 (1994), 1641-1674. CR - [5] Dehghani, N. and Rizvi, S. T., When mutually subisomorphic Baer modules are isomorphic, arxiv: 1909.0344v1 CR - [6] Dung, N. V., Huynh, D. V., Smith, P. F. and Wisbauer, R., Extending modules, Longman, 1994. CR - [7] Herzog, I., Pure injective envelopes, J. Algebra Appl. 4 (2003), 397–402. CR - [8] Rizvi, S. T. and Roman, C. S., On K -nonsingular modules and applications, Comm. Algebra 35 (2007), 2960–2982. UR - https://dergipark.org.tr/en/pub/konuralpjournalmath/article/858467 L1 - https://dergipark.org.tr/en/download/article-file/1502444 ER -