Pseudo-Differential Operator Rings with Armendariz-Like Condition

Manaviyat, R.; Moussavi, A.; Habibi, M.

doi:10.1080/00927872.2010.545962

Cited by 6 publications

(3 citation statements)

References 18 publications

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“…The term Armendariz was introduced by Rege and Chhawchharia [28]. More comprehensive studies of Armendariz rings were carried out recently (see, e.g., [1], [23], [26]). The interest of this notion lies in its natural and useful role in understanding the relation between the annihilators of the ring R and the annihilators of the polynomial ring R[x].…”

Section: Armendariz Rings Of Pseudo-differential Operator Typementioning

confidence: 99%

“…In [23], the authors proved that reduced rings are Armendariz of pseudodifferential operator type, and also provided various rich classes of non-reduced Armendariz rings of pseudo-differential operator type.…”

Section: Armendariz Rings Of Pseudo-differential Operator Typementioning

confidence: 99%

“…In [23], the authors proved that reduced rings (i.e., zero is the only nilpotent element) have this property, and also provided various rich classes of non-reduced 609 Armendariz rings of pseudo-differential operator type. In this paper, we continue to study the relations between the set of annihilators in R and the set of annihilators in R((x −1 ; δ)).…”

Section: Introductionmentioning

confidence: 99%

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On Annihilator Ideals of Pseudo-differential Operator Rings

Manaviyat

Moussavi

2015

Algebra Colloq.

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Let R be a ring with a derivation δ and R((x −1 ; δ)) denote the pseudodifferential operator ring over R. We study the relations between the set of annihilators in R and the set of annihilators in R((x −1 ; δ)). Among applications, it is shown that for an Armendariz ring R of pseudo-differential operator type, the ring R((x −1 ; δ)) is Baer (resp., quasi-Baer, PP, right zip) if and only if R is a Baer (resp., quasi-Baer, PP, right zip) ring. For a δ-weakly rigid ring R, R((x −1 ; δ)) is a left p.q.-Baer ring if and only if R is left p.q.-Baer and every countable subset of left semicentral idempotents of R has a generalized countable join in R.

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Section: Armendariz Rings Of Pseudo-differential Operator Typementioning

confidence: 99%

Section: Armendariz Rings Of Pseudo-differential Operator Typementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Annihilator Ideals of Pseudo-differential Operator Rings

Manaviyat

Moussavi

2015

Algebra Colloq.

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On inverse skew Laurent series extensions of weakly rigid rings

Habibi

2016

Communications in Algebra

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Special properties of differential inverse power series rings

Paykan

Moussavi

2016

J. Algebra Appl.

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In this paper, we continue to study the differential inverse power series ring [Formula: see text], where [Formula: see text] is a ring equipped with a derivation [Formula: see text]. We characterize when [Formula: see text] is a local, semilocal, semiperfect, semiregular, left quasi-duo, (uniquely) clean, exchange, right stable range one, abelian, projective-free, [Formula: see text]-ring, respectively. Furthermore, we prove that [Formula: see text] is a domain satisfying the [Formula: see text] on principal left ideals if and only if so does [Formula: see text]. Also, for a piecewise prime ring (PWP) [Formula: see text] we determine a large class of the differential inverse power series ring [Formula: see text] which have a generalized triangular matrix representation for which the diagonal rings are prime. In particular, it is proved that, under suitable conditions, if [Formula: see text] has a (flat) projective socle, then so does [Formula: see text]. Our results extend and unify many existing results.

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Pseudo-Differential Operator Rings with Armendariz-Like Condition

Cited by 6 publications

References 18 publications

On Annihilator Ideals of Pseudo-differential Operator Rings

On Annihilator Ideals of Pseudo-differential Operator Rings

On inverse skew Laurent series extensions of weakly rigid rings

Special properties of differential inverse power series rings

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