On \phi-Gorenstein homological dimensions
Younes El Haddaoui\,^1, Hwankoo Kim\,^2 and Najib Mahdou\,^3
\,^{1,3} Department of Mathematics, Faculty of Science and Technology, Fez, Morocco.
\,^{2} Division of Computer Engineering, Hoseo University, Asan, Republic of Korea.
Pages 176-197 | Received 20 November 2024, Accepted 28 February 2025, Published 26 January 2026
Abstract
The study of Gorenstein projective and injective modules has been a cornerstone in the field of Gorenstein homological algebra since these concepts were first introduced. This paper marks a significant advancement in the field by demonstrating the integration of \phi-torsion theory into Gorenstein homological algebra. We take this exploration further by introducing and examining the novel concepts of nonnil-Gorenstein projective and injective modules. Our study also extends to the nonnil-Gorenstein projective and injective dimensions of a module, offering a deeper insight into their structure and implications. Furthermore, we delve into the concept of nonnil-Gorenstein global dimension of a ring, unveiling its significance and potential applications. A key application of these innovative concepts is their use in characterizing \phi-von Neumann regular rings. This approach not only adds a new dimension to our understanding of these rings but also highlights the versatility and depth of Gorenstein homological algebra.
Keywords: \phi-torsion theory, \phi-(weak) global dimension of rings, nonnil-Gorenstein global dimension of rings.
MSC numbers: 13A15, 13A18, 13F05, 13G05, 13C20.
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