2024
DOI: 10.1515/forum-2023-0303
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One-sided Gorenstein rings

Lars Winther Christensen,
Sergio Estrada,
Li Liang
et al.

Abstract: Distinctive characteristics of Iwanaga–Gorenstein rings are typically understood through their intrinsic symmetry. We show that several of those that pertain to the Gorenstein global dimensions carry over to the one-sided situation, even without the noetherian hypothesis. Our results yield new relations among homological invariants related to the Gorenstein property, not only Gorenstein global dimensions but also the suprema of projective/injective dimensions of injective/projective modules and finitistic dime… Show more

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Cited by 1 publication
(2 citation statements)
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“…Proof. Due to [53,Theorem 3.7] or [16,Theorem 5.13], we know that G-wgldimpRq ď G-gldimpRq. Thus, any left Gorenstein ring R (i.e., R is of G-gldimpRq ă 8) admits G-wgldimpRq ă 8.…”
Section: Corollary 49 Let R Be a Left Gorenstein Ring The Following A...mentioning
confidence: 99%
See 1 more Smart Citation
“…Proof. Due to [53,Theorem 3.7] or [16,Theorem 5.13], we know that G-wgldimpRq ď G-gldimpRq. Thus, any left Gorenstein ring R (i.e., R is of G-gldimpRq ă 8) admits G-wgldimpRq ă 8.…”
Section: Corollary 49 Let R Be a Left Gorenstein Ring The Following A...mentioning
confidence: 99%
“…It is a refinement of the usual weak global dimension of R, and it is closely related to GgldimpRq. Recently, we have used different methods to prove that GwgldimpRq ď GgldimpRq in [53,Theorem 3.7] and in [16,Theorem 5.13]. In other words, any left Gorenstein ring admits finite Gorenstein weak global dimension.…”
Section: Introductionmentioning
confidence: 99%