Ding projective modules over Morita context rings

References

• Asefa, D.(2021). Gorenstein-projective modules over Morita rings. Algebra Colloq. 28(3):521–532. DOI: 10.1142/S1005386721000407.
   Google Scholar
• Asefa, D.(2021). Gorenstein-projective modules over upper triangular matrix Artin algebras. J. Math. 2021:8127282. DOI: 10.1155/2021/8127282.
   Web of Science ®Google Scholar
• Asefa, D. (2022). Construction of Gorenstein-projective modules over Morita rings. J. Algebra Appl. 2022:2350247. DOI: 10.1142/S021949882350247X.
   Google Scholar
• Asefa, D. (2022). Gorenstein-projective modules over a class of Morita rings. J. Math. 2022:3732360. DOI: 10.1155/2022/3732360.
   Web of Science ®Google Scholar
• Asefa, D. (2022). Strongly Gorenstein-projective modules over rings of Morita contexts. Beitr Algebra Geom. DOI: 10.1007/s13366-022-00675-7.
   Web of Science ®Google Scholar
• Auslander, M., Bridger, M. (1969). Stable Module Theory. Memoirs of the American Mathematical Society, Vol. 94. Providence, RI: American Mathematical Society. DOI: 10.1090/memo/0094.
   Google Scholar
• Auslander, M., Reiten, I. (1991). Applications of contravariantly finite subcategories. Adv. Math. 86:111–152. DOI: 10.1016/0001-8708(91)90037-8.
   Web of Science ®Google Scholar
• Avramov, L. L., Martsinkovsky, A. (2002). Absolute,relative, and Tate cohomology of modules of finite Gorenstein dimension. Proc. London Math. Soc. 85:393–440. DOI: 10.1112/S0024611502013527.
   Web of Science ®Google Scholar
• Bass, H. (1962). The Morita Theorems, Mimeographed Notes. University of Oregon.
   Google Scholar
• Beligiannis, A. (2005). Cohen-Macaulay modules, (co)torsion pairs and virtually Gorenstein algebras. J. Algebra 288:137–211. DOI: 10.1016/j.jalgebra.2005.02.022.
   Web of Science ®Google Scholar
• Beligiannis, A. (2011). On algebras of finite cohen-Macaulay type. Adv. Math. 226:1973–2019. DOI: 10.1016/j.aim.2010.09.006.
   Web of Science ®Google Scholar
• Ding, N. Q., Li, Y. L., Mao, L. X. (2009). Strongly Gorenstein flat modules. J. Aust. Math. Soc. 86:323–338. DOI: 10.1017/S1446788708000761.
   Web of Science ®Google Scholar
• Enochs, E. E., Jenda, O. M. G. (1995). Gorenstein injective and projective modules. Math. Z. 220:611–633. DOI: 10.1007/BF02572634.
   Web of Science ®Google Scholar
• Enochs, E. E., Cortés-Izurdiaga, M. Torrecillas, B. (2014). Gorenstein conditions over triangular matrix rings. J. Pure Appl. Algebra 218:1544–1554. DOI: 10.1016/j.jpaa.2013.12.006.
   Web of Science ®Google Scholar
• Gao, N., Psaroudakis, C. (2017). Gorenstein homological aspects of monomorphism categories via morita rings. Algebras Represent. Theory 20:487–529. DOI: 10.1007/s10468-016-9652-1.
   Web of Science ®Google Scholar
• Gao, N., Ma, J., Liu, X. Y. (2021). RSS equivalences over a class of Morita rings. J. Algebra 573:336–363. DOI: 10.1016/j.jalgebra.2020.12.037.
   Web of Science ®Google Scholar
• Gillespie, J. (2010). Model structures on modules over Ding-Chen rings. Homol. Homotopy Appl. 12:61–73. DOI: 10.4310/HHA.2010.v12.n1.a6.
   Web of Science ®Google Scholar
• Green, E. L. (1982). On the representation theory of rings in matrix form. Pac. J. Math. 100(1):123–138. DOI: 10.2140/pjm.1982.100.123.
   Web of Science ®Google Scholar
• Green, E. L., Psaroudakis, C. (2014). On artin algebras arising from morita contexts, Algebras Represent. Theory 17(5):1485–1525. DOI: 10.1007/s10468-013-9457-4.
   Web of Science ®Google Scholar
• Guo, Q. (2023). Gorenstein-projective modules via total complexes. Commun. Algebra 51(1):384–392. DOI: 10.1080/00927872.2022.2099553.
   Web of Science ®Google Scholar
• Guo, Q. Q., Xi, C. C. Gorenstein projective modules over rings of Morita contexts. DOI: 10.48550/arXiv.2205.10567v1.
   Google Scholar
• Happel, D. (1991). On Gorenstein algebras. In: Representation Theory of Finite Groups and Finite-Dimensional Algebras. Progress in Mathematics, Vol. 95. Basel: Birkhäuser, pp. 389–404.
   Google Scholar
• Holm, H. (2004). Gorenstein homological dimensions. J. Pure Appl. Algebra 189:167–193. DOI: 10.1016/j.jpaa.2003.11.007.
   Web of Science ®Google Scholar
• Iacob, A. (2021). Ding injective modules. Commun. Algebra 49:2901–2905. DOI: 10.1080/00927872.2021.1883640.
   Web of Science ®Google Scholar
• Krylov, P. A., Tuganbaev, A. A. (2010). Modules over formal matrix rings. J. Math. Sci. 171:248–295. DOI: 10.1007/s10958-010-0133-5.
   Google Scholar
• Krylov, P., Tuganbaev, A. (2017). Formal Matrices. Cham: Springer.
   Google Scholar
• Luo, X. H., Zhang, P. (2017). Separated monic representations I: Gorenstein-projective modules. J. Algebra 479:1–34. DOI: 10.1016/j.jalgebra.2017.01.038.
   Web of Science ®Google Scholar
• Ma, Y., Lu, J., Li, H., Hu, J. How to construct Gorenstein projective modules relative to complete duality pairs over Morita rings. https://arxiv.org/pdf/2203.08673.pdf
   Google Scholar
• Mao, L. X. (2020). Strongly Gorenstein projective, injective and flat modules over formal triangular matrix rings. Bull. Math. Soc. Sci. Math. Roumanie 63(3):271–283.
   Google Scholar
• Mao, L. X. (2020). Gorenstein flat modules and dimensions over formal triangular matrix rings. J. Pure Appl. Algebra 224:106207. DOI: 10.1016/j.jpaa.2019.106207.
   Web of Science ®Google Scholar
• Mao, L. X. (2023). Gorenstein flat modules over some Morita context rings. J. Algebra Appl. 2450096. DOI: 10.1142/S0219498824500968.
   Web of Science ®Google Scholar
• Mao, L. X. (2020). Duality pairs and FP-injective modules over formal triangular matrix rings. Commun. Algebra 48(12):5296–5310. DOI: 10.1080/00927872.2020.1786837.
   Web of Science ®Google Scholar
• Mao, L. X. (2022). Ding modules and dimensions over formal triangular matrix rings. Rend. Sem. Mat. Univ. Padova. http://rendiconti.math.unipd.it/forthcoming/downloads/Mao2020.pdf. DOI: 10.4171/RSMUP/100.
   Web of Science ®Google Scholar
• Mao, L. X., Ding, N. Q. (2008). Gorenstein FP-injective and Gorenstein flat modules. J. Algebra Appl. 7:491–506. DOI: 10.1142/S0219498808002953.
   Web of Science ®Google Scholar
• Müller, M. (1987). Rings of quotients of generalized matrix rings. Commun. Algebra 15:1991–2015.
   Web of Science ®Google Scholar
• Ringel, C. M., Zhang, P. (2017). Representations of quivers over the algebra of dual numbers. J. Algebra 475:327–360. DOI: 10.1016/j.jalgebra.2016.12.001.
   Web of Science ®Google Scholar
• Xiong, B. L., Zhang, P. (2012). Gorenstein-projective modules over triangular matrix Artin algebras. J. Algebra Appl. 11(4):1250066. DOI: 10.1142/S0219498812500661.
   Web of Science ®Google Scholar
• Yang, G. (2012). Homological properties of modules over Ding-Chen rings. J. Korean Math. Soc. 49:31–47. DOI: 10.4134/JKMS.2012.49.1.031.
   Web of Science ®Google Scholar
• Yang, G., Liu, Z. K., Liang, L. (2013). Ding projective and Ding injective modules. Algebra Colloq. 20:601–612. DOI: 10.1142/S1005386713000576.
   Web of Science ®Google Scholar
• Yan, M. Q., Yao, H. L. (2020). Pure projective modules and FP-injective modules over Morita rings. Front. Math. China 15(6):1265–1293. DOI: 10.1007/s11464-020-0877-2.
   Web of Science ®Google Scholar
• Zhang, P. (2011). Monomorphism Categories, cotilting theory, and Gorenstein-projective modules. J. Algebra 339:181–202. DOI: 10.1016/j.jalgebra.2011.05.018.
   Web of Science ®Google Scholar
• Zhang, P. (2013). Gorenstein-projective modules and symmetric recollements. J. Algebra 388:65–80. DOI: 10.1016/j.jalgebra.2013.05.008.
   Web of Science ®Google Scholar
• Zhang, P., Xiong, B. L. (2019). Separated monic representations II: Frobenius subcategories and RSS equivalences. Trans. Amer. Math. Soc. 372(2):981–1021. DOI: 10.1090/tran/7622.
   Web of Science ®Google Scholar