On (Strongly) Gorenstein Von Neumann Regular Rings

Mahdou, Najib; Tamekkante, Mohammed; Yassemi, Siamak

doi:10.1080/00927872.2010.501773

Cited by 15 publications

(3 citation statements)

References 19 publications

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“…Bennis [3] characterized IF rings in terms of the Gorenstein weak global dimension, which at that point was not known to be symmetric. In the commutative case, where this distinction is irrelevant, the characterization was also obtained by Mahdou, Tamekkante, and Yassemi [22]. Here we use the Gorenstein flat-cotorsion dimension to characterize left-IF rings; Bennis' characterization [3,Proposition 2.4] is recovered in Theorem 2.2.…”

Section: If Ringsmentioning

confidence: 92%

Five theorems on Gorenstein global dimensions

Christensen¹,

Estrada²,

Thompson³

2022

Preprint

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Section: If Ringsmentioning

confidence: 92%

Five theorems on Gorenstein global dimensions

Christensen¹,

Estrada²,

Thompson³

2022

Preprint

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“…Considerable work, part of it summarized in Glaz's book [9] and Huckaba's book [16], has been concerned with trivial ring extensions. These have proven to be useful in solving many open problems and conjectures for various contexts in (commutative and non-commutative) ring theory, see for instance [9,16,18,23,24].…”

Section: Localization Of Prüfer Conditionsmentioning

confidence: 99%

Transfer of Prufer-like conditions

Bakkari¹

2013

GJOM

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“…Recall that a ring R is called Gorenstein Von Neumann regular [14] if wGgldim(R) = 0 (that is every R-module is Gorenstein flat).…”

Section: Introductionmentioning

confidence: 99%

Note on the Dw Rings

Tamekkante¹,

Assaad²,

Bouba³

2019

International Electronic Journal of Algebra

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In this paper we are mainly concerned with DW rings, i.e., rings in which every ideal is a w-ideal. We give some new classes of DW rings and we show how the concept of DW domains is used to characterize Prüfer domains and Dedekind domains. Namely, we prove that a ring is a Prüfer domain (resp., Dedekind domain) if and only if it a coherent (resp., Noetherian) DW domain with finite weak global dimension. (2010): 13D05, 13D07, 13H05 A commutative ring is called a DW ring if every ideal of R is a w-ideal. Over a domain this last definition coincides with the definition of DW domain in [16]. In Section 2, we give some new classes of DW rings. Section 3 gives new characterizations of Krull domains, Dedekind domains and PvMDs. Throughout, all rings considered are commutative with unity and all modules are unital. Let R be a ring and M be an R-module. As usual, we use pd R (M ), id R (M ), and fd R (M ) to denote, respectively, the classical projective dimension, injective dimension, and flat dimension of M , and wdim(R) and gldim(R) to denote, respectively, the weak and global homological dimensions of R. Mathematics Subject Classification On DW ringsLet w-Max(R) denote the set of w-ideals of R maximal among proper integral w-ideals of R (maximal w-ideals). By [25, Proposition 3.8], every maximal w-ideal is prime. Let M and N be R-modules and let f : M → N be a homomorphism.

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On (Strongly) Gorenstein Von Neumann Regular Rings

Cited by 15 publications

References 19 publications

Five theorems on Gorenstein global dimensions

Five theorems on Gorenstein global dimensions

Transfer of Prufer-like conditions

Note on the Dw Rings

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