Gorenstein projective modules over Milnor squares of rings

Qianqian Guo; Qianqian Guo

doi:10.3934/math.20241384

AIMS Mathematics

2024, Volume 9, Issue 10: 28526-28541. doi: 10.3934/math.20241384

Previous Article Next Article

Research article

Gorenstein projective modules over Milnor squares of rings

Qianqian Guo ^,

School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, MOE, Beijing Normal University, Beijing 100875, China

Received: 27 July 2024 Revised: 19 September 2024 Accepted: 24 September 2024 Published: 08 October 2024
MSC : 16E05, 18G05, 18G25

We construct a class of Gorenstein-projective modules over Milnor squares of rings. As an application, we obtain Gorenstein-projective modules over Morita context rings with two bimodule homomorphisms zero in the general setting instead of Artin algebras or Noetherian rings.
- Gorenstein-projective module,
- Milnor square of ring,
- Morita context ring,
- fiber product category
Citation: Qianqian Guo. Gorenstein projective modules over Milnor squares of rings[J]. AIMS Mathematics, 2024, 9(10): 28526-28541. doi: 10.3934/math.20241384

Related Papers:

Abstract

We construct a class of Gorenstein-projective modules over Milnor squares of rings. As an application, we obtain Gorenstein-projective modules over Morita context rings with two bimodule homomorphisms zero in the general setting instead of Artin algebras or Noetherian rings.

References

[1]	E. E. Enochs, M. Cortés-Izurdiaga, B. Torrecillas, Gorenstein conditions over triangular matrix rings, J. Pure Appl. Algebra, 218 (2014), 1544–1554. http://doi.org/10.1016/j.jpaa.2013.12.006 doi: 10.1016/j.jpaa.2013.12.006
[2]	E. E. Enochs, O. M. G. Jenda, Gorenstein injective and projective modules, Math. Z., 220 (1995), 611–633. http://doi.org/10.1007/BF02572634 doi: 10.1007/BF02572634
[3]	H. Eshraghi, R. Hafezi, S. Salarian, Z. W. Li, Gorenstein projective modules over triangular matrix rings, Algebra Colloq., 23 (2016), 97–104. http://doi.org/10.1142/S1005386716000122 doi: 10.1142/S1005386716000122
[4]	A. Facchini, P. Vámos, Injective modules over pullbacks, J. Lond. Math. Soc., s2-31 (1985), 425–438. http://doi.org/10.1112/jlms/s2-31.3.425 doi: 10.1112/jlms/s2-31.3.425
[5]	N. Gao, C. Psaroudakis, Gorenstein homological aspects of monomorphism categories via Morita rings, Algebr. Represent. Theor., 20 (2017), 487–529. http://doi.org/10.1007/s10468-016-9652-1 doi: 10.1007/s10468-016-9652-1
[6]	E. L. Green, C. Psaroudakis, On Artin algebras arising from Morita contexts, Algebr. Represent. Theor., 17 (2014), 1485–1525. http://doi.org/10.1007/s10468-013-9457-4 doi: 10.1007/s10468-013-9457-4
[7]	Q. Q. Guo, C. C. Xi, Gorenstein projective modules over rings of Morita contexts, Sci. China Math., in press. http://doi.org/10.1007/s11425-022-2206-8
[8]	D. Herbara, P. Prihoda, Infinitely generated projective modules over pullbacks of rings, Trans. Amer. Math. Soc., 366 (2014), 1433–1454. http://doi.org/10.1090/S0002-9947-2013-05798-4 doi: 10.1090/S0002-9947-2013-05798-4
[9]	H. Holm, Gorenstein homological dimensions, J. Pure Appl. Algebra, 189 (2004), 167–193. http://doi.org/10.1016/j.jpaa.2003.11.007 doi: 10.1016/j.jpaa.2003.11.007
[10]	W. Hu, X.-H. Luo, B.-L. Xiong, G. D. Zhou, Gorenstein projective bimodules via monomorphism categories and filtration categories, J. Pure Appl. Algebra, 223 (2019), 1014–1039. http://doi.org/10.1016/j.jpaa.2018.05.012 doi: 10.1016/j.jpaa.2018.05.012
[11]	P. A. Krylov, A. A. Tuganbaev, Modules over formal matrix rings, J. Math. Sci., 171 (2010), 248–295. http://doi.org/10.1007/s10958-010-0133-5 doi: 10.1007/s10958-010-0133-5
[12]	L. S. Levy, Modules over pullbacks and subdirect sums, J. Algebra, 71 (1981), 50–61. http://doi.org/10.1016/0021-8693(81)90106-X doi: 10.1016/0021-8693(81)90106-X
[13]	J. Milnor, Introduction to algebraic K-theory, Princeton: Princeton University Press, 1972. https://doi.org/10.1515/9781400881796

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)