Principally Quasi-Baer Rings

Birkenmeier, Gary F.; Kim, Jin Yong; Park, Jae Keol

doi:10.1081/agb-100001530

Cited by 146 publications

(69 citation statements)

References 29 publications

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“…R r X   R l X ) denote a right (resp.,left) annihilator of X in R. A ring R is called right principally quasi-Baer (simply, right p.q.-Baer) if the right annihilator of every principal right ideal of R is generated, as a right ideal by an idempotent of R in [1]. A left principally quasi-Baer (simply, left p.q.-Baer) ring is defined similarly.…”

Section:  mentioning

confidence: 99%

“…Right p.q.-Baer rings have been initially studied in [1]. For more details on (right) p.q.-Baer rings, see [1][2][3][4][5][6]. A ring R is called quasi-Baer if the right annihilator of every right ideal is generated, as a right ideal by an idempotent of R in [7] (see also [8].…”

Section:  mentioning

confidence: 99%

“…A left principally quasi-Baer (simply, left p.q.-Baer) ring is defined similarly. Right p.q.-Baer rings have been initially studied in [1]. For more details on (right) p.q.-Baer rings, see [1][2][3][4][5][6].…”

Section:  mentioning

confidence: 99%

See 2 more Smart Citations

The p.q.-Baer Property of Skew Group Rings under Finite Group Action*

Li¹,

Jin²

2013

APM

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Section:  mentioning

confidence: 99%

Section:  mentioning

confidence: 99%

See 1 more Smart Citation

The p.q.-Baer Property of Skew Group Rings under Finite Group Action*

Li¹,

Jin²

2013

APM

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“…From [4], a ring R is called right (resp., left) principally quasi-Baer (or simply, right (resp., left) p.q.-Baer) if the right (resp., left) annihilator of a principal right (resp., left) ideal of R is generated by an idempotent. R is called a p. [2,4,6,7,8]. In [9], it was proved that for a σ-rigid ring R, a ring R is (quasi- …”

Section: Applicationsmentioning

confidence: 99%

On Quasi-Rigid Ideals and Rings

Hong¹,

Kim²,

Kwak³

2010

Bulletin of the Korean Mathematical Society

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Abstract. Let σ be an endomorphism and I a σ-ideal of a ring R. Pearson and Stephenson called I a σ-semiprime ideal if whenever A is an ideal of R and m is an integer such that Aσ t (A) ⊆ I for all t ≥ m, then A ⊆ I, where σ is an automorphism, and Hong et al. called I a σ-rigid ideal if aσ(a) ∈ I implies a ∈ I for a ∈ R. Notice that R is called a σ-semiprime ring (resp., a σ-rigid ring) if the zero ideal of R is a σ-semiprime ideal (resp., a σ-rigid ideal). Every σ-rigid ideal is a σ-semiprime ideal for an automorphism σ, but the converse does not hold, in general. We, in this paper, introduce the quasi σ-rigidness of ideals and rings for an automorphism σ which is in between the σ-rigidness and the σ-semiprimeness, and study their related properties. A number of connections between the quasi σ-rigidness of a ring R and one of the Ore extension R[x; σ, δ] of R are also investigated. In particular, R is a (principally) quasi-Baer ring if and only if R[x; σ, δ] is a (principally) quasi-Baer ring, when R is a quasi σ-rigid ring. DefinitionsLet σ be an endomorphism of a ring R, the additive map δ :

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“…Recently, Birkenmeier et al [5] called a ring R right (resp. left) principally quasi-Baer [or simply right (resp.…”

Section: Introductionmentioning

confidence: 99%

On Quasi-Baer and p.q.-Baer Modules

Basser

Harmanci

2009

Kyungpook mathematical journal

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Abstract. For an endomorphism α of R, in [1], a module MR is called α-compatible if, for any m ∈ M and a ∈ R, ma = 0 iff mα(a) = 0, which are a generalization of α-reduced modules. We study on the relationship between the quasi-Baerness and p.q.-Baer property of a module MR and those of the polynomial extensions (including formal skew power series, skew Laurent polynomials and skew Laurent series). As a consequence we obtain a generalization of [2] and some results in [9]. In particular, we show: for an α-compatible module MR (1)

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Principally Quasi-Baer Rings

Cited by 146 publications

References 29 publications

The p.q.-Baer Property of Skew Group Rings under Finite Group Action*

The p.q.-Baer Property of Skew Group Rings under Finite Group Action*

On Quasi-Rigid Ideals and Rings

On Quasi-Baer and p.q.-Baer Modules

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