Pure-direct-objects in categories: transfer via functors

References

• Alizade, R., Toksoy S. E. (2022). Pure-direct-projective modules. J. Algebra Appl. DOI: 10.1142/S0219498824500105.
   Web of Science ®Google Scholar
• Bourbaki, N. (1972). Elements of Mathematics, Commutative Algebra, Advanced Book Program. Reading, MA: Addison-Wesley Publishing Company. Originally published as: Bourbaki, N. (1969). Elements De Mathematique, Algebre Commutative, Hermann, Paris.
   Google Scholar
• Buttler, M. C. R., Horrocks, G. (1961). Classes of extensions and resolutions. Phil. Trans. Royal Soc. of London, Ser. A. 254(1039):155–222.
   Google Scholar
• Castaño Iglesias, F., Gómez-Torecillas, J., Wisbauer, R. (2003). Adjoint functors and equivalences of subcategories. Bull. Sci. Math. 127(5):379–395.
   Web of Science ®Google Scholar
• Clark, J. (1998). On purely extending modules. Abelian Groups and Modules: Proceedings of the International Conference in Dublin, Trends Math, Basel: Birkhauser, pp. 353–358.
   Google Scholar
• Clark, J., Wisbauer, R. (2011). Idempotent monads and *-functors. J. Pure Appl. Algebra 215:145–153.
   Web of Science ®Google Scholar
• Cohn, P. M. (1959). On the free product of associative rings. Math. Z. 71:380–398.
   Google Scholar
• Crawley-Boevey, W. (1994). Locally finitely presented additive categories. Commun. Algebra 22(5):1641–1674.
   Web of Science ®Google Scholar
• Crivei, S. (2008). ∑-extending modules, ∑ -lifting modules, and proper classes. Commun. Algebra 36(2):529–545.
   Web of Science ®Google Scholar
• Crivei, S. (2011). On Krull-Schmidt finitely accessible categories. Bull. Aust. Math. Soc. 84:90–97.
   Web of Science ®Google Scholar
• Crivei, S., Olteanu, G. (2018). Rickart and dual Rickart objects in abelian categories: transfer via functors. Appl. Categ. Struct. 26(4):681–698.
   Web of Science ®Google Scholar
• Crivei, S., Keskin Tütüncü, D., Tribak, R. (2020). Transfer of splitness with respect to a fully invariant short exact sequence in abelian categories. Commun. Algebra 48(6):2639–2654.
   Web of Science ®Google Scholar
• Crivei, S., Keskin Tütüncü, D., Tribak, R. (2020). Baer-Kaplansky classes in categories: transfer via functors. Commun. Algebra 48(7):3157–3169.
   Web of Science ®Google Scholar
• Crivei, S., Radu, S. M. (2022). Transfer of CS-Rickart and dual CS-Rickart properties via functors between abelian categories. Quaest. Math. 45(7):993–1011. DOI: 10.2989/16073606.2021.1925990.
   Web of Science ®Google Scholar
• Dăscălescu, S., Năstăsescu, C., Raianu, Ş. (2001). Hoph Algebras. An Introduction. Pure and Applied Mathematics, Vol. 235. New York: Marcel Dekker, Inc.
   Google Scholar
• Dyckhoff, R., Tholen, W. (1987). Exponentiable morphisms, partial products and pullback complements. J. Pure Appl. Algebra 49(1–2):103–116.
   Web of Science ®Google Scholar
• Gómez Pardo, J. L., Guil Asensio, P. A. (1997). Indecomposable decompositions of finitely presented pure-injective modules. J. Algebra 192(1):200–208.
   Web of Science ®Google Scholar
• Goodearl, K. G. (1976). Ring Theory: Nonsingular Rings and Modules. New York: Marcel Dekker, Inc.
   Google Scholar
• Keskin Tütüncü, D., Kaleboğaz, B. (2022). D4-objects in abelian categories: transfer via functors. Commun. Algebra 50(2):687–698.
   Web of Science ®Google Scholar
• Maurya, S. K., Das, S., Alagöz, Y. (2022). Pure-direct-injective modules. Lobachevskii J. Math. 43(2):416–428.
   Web of Science ®Google Scholar
• Nicholson, W. K. (1976). Semiregular modules and rings. Can. J. Math. XXVIII(5):1105–1120. DOI: 10.4153/CJM-1976-109-2.
   Web of Science ®Google Scholar
• Pareigis, B. (1970). Categories and Functors. Pure and Applied Mathematics A Series of Monographs and Textbooks. New York and London: Academic Press.
   Google Scholar
• Prest, M. (2011). Definable Additive Categories: Purity and Model Theory. Memories of the American Mathematical Society, Vol. 210. Providence, RI: American Mathematical Society. DOI: 10.1090/S0065-9266-2010-00593-3.
   Google Scholar
• Prüfer, H. (1923). Untersuchungen über die Zerlegbarkeit der abzählbaren primären Abelschen Gruppen. Mathematische Zeitschrift 17:35–61.
   Google Scholar
• Stenström, B. T. (1966). Pure submodules. Ark. Mat. 7(10):159–171.
   Google Scholar
• Stenström, B. T. (1968). Purity in functor categories. J. Algebra 8:352–361. DOI: 10.1016/0021-8693(68)90064-1.
   Web of Science ®Google Scholar
• Stenström, B. (1975). Rings of Quotients. An Introduction to Methods of Ring Theory, Berlin, Heidelberg, New York: Springer-Verlag.
   Google Scholar
• Takeuchi, M. (1977). Morita theorems for categories of comodules. J. Fac. Sci. Univ. Tokyo 24:629–644.
   Google Scholar
• Toksoy, S. E. (2021). Purely Rickart and dual purely Rickart objects in Grothendieck categories. Mediterr. J. Math. 18(5):Paper No. 216, 25 pp. DOI: 10.1007/s00009-021-01859-6.
   Web of Science ®Google Scholar
• Walker, C. L. (1966). Relative homological algebra and abelian groups. Illinois J. Math. 10:186–209. DOI: 10.1215/ijm/1256055101.
   Google Scholar
• Wisbauer, R. (1991). Foundations of Module and Ring Theory. A Handbook for Study and Research, Reading: Gordon and Breach Science Publishers.
   Google Scholar