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.
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.
Keywords
Schrödinger-Bernstein problem Pseudo-Injective object Pure Goldie dimension Finitely accessible additive category
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.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Submission Date | May 7, 2020 |
| Acceptance Date | December 19, 2020 |
| Publication Date | June 30, 2021 |
| DOI | https://doi.org/10.31801/cfsuasmas.733614 |
| IZ | https://izlik.org/JA59AE57LY |
| Published in Issue | Year 2021 Volume: 70 Issue: 1 |
Cite
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