References
- Agayev, N., Koşan, T., Leghwel, A., Harmanci, A. (2006). Duo modules and duo rings. Far East J. Math. Sci. 20:341–346.
- Asgari, S., Haghany, A. (2015). t-Rickart and dual t-Rickart modules. Algebra Colloq. 22(spec01):849–870. DOI: https://doi.org/10.1142/S1005386715000735.
- Bican, L., Kepka, T., Nemec, P. (1982). Rings, Modules and Preradicals. New York, NY: Marcel Dekker.
- Bühler, T. (2010). Exact categories. Expo. Math. 28(1):1–69. DOI: https://doi.org/10.1016/j.exmath.2009.04.004.
- Calci, T. P., Halicioglu, S., Harmanci, A. (2017). Modules having Baer summands. Commun. Algebra 45(11):4610–4621. DOI: https://doi.org/10.1080/00927872.2016.1273360.
- Chase, S. U. (1960). Direct products of modules. Trans. Amer. Math. Soc. 97(3):457–473. DOI: https://doi.org/10.1090/S0002-9947-1960-0120260-3.
- 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. DOI: https://doi.org/10.1080/00927872.2020.1721732.
- Crivei, S., Keskin Tütüncü, D., Tribak, R. (2021). Split objects with respect to a fully invariant short exact sequence in abelian categories. Rend. Sem. Mat. Univ. Padova.
- Crivei, S., Kör, A. (2016). Rickart and dual Rickart objects in abelian categories. Appl. Categor. Struct. 24(6):797–824. DOI: https://doi.org/10.1007/s10485-015-9405-z.
- Crivei, S., Olteanu, G. (2018). Rickart and dual Rickart objects in abelian categories: Transfer via functors. Appl. Categor. Struct. 26(4):681–698. DOI: https://doi.org/10.1007/s10485-017-9509-8.
- Crivei, S., Olteanu, G. (2018). Strongly Rickart objects in abelian categories. Commun. Algebra 46(10):4326–4343. DOI: https://doi.org/10.1080/00927872.2018.1439046.
- Crivei, S., Olteanu, G. (2018). Strongly Rickart objects in abelian categories: Applications to strongly regular objects and Baer objects. Commun. Algebra 46(10):4426–4447. DOI: https://doi.org/10.1080/00927872.2018.1444171.
- Crivei, S., Prest, M., Torrecillas, B. (2010). Covers in finitely accessible categories. Proc. Amer. Math. Soc. 138(04):1213–1221. DOI: https://doi.org/10.1090/S0002-9939-09-10178-8.
- Cuadra, J., Simson, D. (2007). Flat comodules and perfect coalgebras. Commun. Algebra 35(10):3164–3194. DOI: https://doi.org/10.1080/00914030701409908.
- Dăscălescu, S., Năstăsescu, C., Raianu, Ş. (2001). Hopf Algebras. An Introduction. New York, NY: Marcel Dekker.
- Dăscălescu, S., Năstăsescu, C., Tudorache, A., Dăuş, L. (2006). Relative regular objects in categories. Appl. Categor. Struct. 14(5–6):567–577. DOI: https://doi.org/10.1007/s10485-006-9048-1.
- Ebrahimi Atani, S., Khoramdel, M., Dolati Pish Hesari, S. (2012). T-Rickart modules. Colloq. Math. 128(1):87–100. DOI: https://doi.org/10.4064/cm128-1-8.
- Ebrahimi Atani, S., Khoramdel, M., Dolati Pish Hesari, S. (2014). On strongly extending modules. Kyungpook Math. J. 54(2):237–247. DOI: https://doi.org/10.5666/KMJ.2014.54.2.237.
- Ebrahimi Atani, S., Khoramdel, M., Dolati Pish Hesari, S. (2016). T-dual Rickart modules. Bull. Iranian Math. Soc. 42:627–642.
- Goodearl, K. R. (1976). Ring Theory: Nonsingular Rings and Modules. New York, NY: Marcel Dekker.
- Kaplansky, I. (1952). Modules over Dedekind rings and valuation rings. Trans. Amer. Math. Soc. 72(2):327–340. DOI: https://doi.org/10.1090/S0002-9947-1952-0046349-0.
- Kelly, G. M. (1969). Monomorphisms, epimorphisms and pull-backs. J. Aust. Math. Soc. 9(1–2):124–142. DOI: https://doi.org/10.1017/S1446788700005693.
- Keskin Tütüncü, D., Tribak, R. (2010). On dual Baer modules. Glasgow Math. J. 52(2):261–269. DOI: https://doi.org/10.1017/S0017089509990334.
- Lee, G., Rizvi, S. T., Roman, C. (2010). Rickart modules. Commun. Algebra 38(11):4005–4027. DOI: https://doi.org/10.1080/00927872.2010.507232.
- Lee, G., Rizvi, S. T., Roman, C. (2011). Dual Rickart modules. Commun. Algebra 39(11):4036–4058. DOI: https://doi.org/10.1080/00927872.2010.515639.
- Lee, G., Rizvi, S. T., Roman, C. (2012). Direct sums of Rickart modules. J. Algebra 353(1):62–78. DOI: https://doi.org/10.1016/j.jalgebra.2011.12.003.
- Mitchell, B. (1965). Theory of Categories. New York, NY: Academic Press.
- Năstăsescu, C., Torrecillas, B. (2004). The splitting problem for coalgebras. J. Algebra 281(1):144–149. DOI: https://doi.org/10.1016/j.jalgebra.2004.06.004.
- Özcan, A. Ç., Harmanc I. A., Smith, P. F. (2006). Duo modules. Glasgow Math. J. 48(03):533–545. DOI: https://doi.org/10.1017/S0017089506003260.
- Rizvi, S. T., Roman, C. (2004). Baer and quasi-Baer modules. Commun. Algebra 32(1):103–123. DOI: https://doi.org/10.1081/AGB-120027854.
- Rizvi, S. T., Roman, C. (2009). On direct sums of Baer modules. J. Algebra 321(2):682–696. DOI: https://doi.org/10.1016/j.jalgebra.2008.10.002.
- Stenström, B. (1975). Rings of Quotients. Grundlehren Der Math, Vol. 127. Berlin: Springer.
- Teply, M. L. (1975). Generalizations of the simple torsion class and the splitting properties. Can. J. Math. 27(5):1056–1074. DOI: https://doi.org/10.4153/CJM-1975-111-9.
- Ungor, B., Halicioglu, S., Harmanci, A. (2016). Modules in which inverse images of some submodules are direct summands. Commun. Algebra 44(4):1496–1513. DOI: https://doi.org/10.1080/00927872.2015.1027355.
- Ungor, B., Halicioglu, S., Harmanci, A. (2018). A dual approach to the theory of inverse split modules. J. Algebra Appl. 17(08):1850148. DOI: https://doi.org/10.1142/S0219498818501487.
- Wang, Y. (2017). Strongly lifting modules and strongly dual Rickart modules. Front. Math. China 12(1):219–229. DOI: https://doi.org/10.1007/s11464-016-0599-7.
- Wisbauer, R. (1991). Foundations of Module and Ring Theory. Reading: Gordon and Breach.