Pseudo pure-injective objects

Yıl 2021, Cilt: 70 Sayı: 1, 265 - 268, 30.06.2021

Mustafa Kemal Berktaş

https://doi.org/10.31801/cfsuasmas.733614

Cited By: 1

Öz

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.

Anahtar Kelimeler

Schrödinger-Bernstein problem, Pseudo-Injective object, Pure Goldie dimension, Finitely accessible additive category

Kaynakça

• 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.