On Artiness of Right CF Rings

Chen, Jianlong; Li, Wenxi

doi:10.1081/agb-200034189

Cited by 17 publications

(2 citation statements)

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“…R is called a right finitely Σ-C2 ring if every finite direct sum copies of R R is a C2 module. Right finitely Σ-C2 rings are also called strongly right C2 rings (see [3,Definition 2.2]). In this article, we define a ring R to be right countably…”

Section: Introductionmentioning

confidence: 99%

On countably $Σ$-C2 rings

Shen¹,

Chen²

2010

Preprint

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Let R be a ring. R is called a right countably Σ-C2 ring if every countable direct sum copies of R R is a C2 module. The following are equivalent for a ring R: (1) R is a right countably Σ-C2 ring. ( 2) The column finite matrix ring CFM N (R) is a right C2 (or C3) ring. (3) Every countable direct sum copies of R R is a C3 module. (4) Every projective right R-module is a C2 (or C3) module. (5) R is a right perfect ring and every finite direct sum copies of R R is a C2 (or C3) module. This shows that right countably Σ-C2 rings are just the rings whose right finitistic projective dimension rF P D(R)=sup{P d R (M)| M is a right R-module with P d R (M) < ∞}=0, which were introduced by Hyman Bass in 1960.

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Section: Introductionmentioning

confidence: 99%

On countably $Σ$-C2 rings

Shen¹,

Chen²

2010

Preprint

Self Cite

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“…(4) ⇒ (1). Note that right MGP-injectivity implies that J(R) = Z r by [2] (Theorem 3.4(2)), so R is right artinian by [11] (Corollary 2.9). Since R is right and left mininjective, by [9] Proof.…”

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confidence: 99%

Some results on MP-injectivity and MGP-injectivity of rings and modules

Zhu

2012

Ukr Math J

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We study MP-injective rings and MGP-injective rings satisfying some additional conditions. Using the concepts of MP-injectivity and MGP-injectivity of rings and modules, we present some new characterizations of QFrings, semisimple Artinian rings, strongly regular rings, and simple Artinian rings. Вивчаються MP-iн'єктивнi та MGP-iн'єктивнi кiльця, що задовольняють деякi додатковi умови. Iз застосуванням понять MP-iн'єктивностi та MGP-iн'єктивностi кiлець та модулiв наведено новi характеризацiї QF-кiлець, напiвпростих кiлець Артiна, сильно регулярних кiлець та простих кiлець Артiна.

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When Maximal Linearly Independent Subsets of a Free Module Have the Same Cardinality?

Kourki

Modules and Comodules

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On Artiness of Right CF Rings

Abstract: Let R be a ring. We prove that every right CF ring is right artinian under the left perfect or strongly right C2 condition. We also show that a right noetherian, left P-injective, left CS-ring is QF.

Cited by 17 publications

References 17 publications

On countably $Σ$-C2 rings

On countably $Σ$-C2 rings

Some results on MP-injectivity and MGP-injectivity of rings and modules

When Maximal Linearly Independent Subsets of a Free Module Have the Same Cardinality?

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