On a conjecture posed by Benhissi and Koja

Dong Kyu Kim; Jung Wook Lim

doi:10.1080/00927872.2020.1721733

On a conjecture posed by Benhissi and Koja

Dong Kyu Kim, Jung Wook Lim

Kyungpook National University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let (Formula presented.) = (R_n)_n≥0 be an ascending chain of commutative rings with identity and (Formula presented.) (resp., (Formula presented.)) the generalized composite Hurwitz series ring (resp., generalized composite Hurwitz polynomial ring). In this paper, we completely characterize when the rings (Formula presented.) and (Formula presented.) are PS-rings. More precisely, we show that (Formula presented.) and (Formula presented.) are always PS-rings. This is an affirmative answer to the question raised by Benhissi and Koja. Communicated by Silvana Bazzoni.

Original language	English
Pages (from-to)	2655-2661
Number of pages	7
Journal	Communications in Algebra
Volume	48
Issue number	6
DOIs	https://doi.org/10.1080/00927872.2020.1721733
State	Published - 2 Jun 2020

Keywords

Annihilator
generalized composite Hurwitz polynomial ring
generalized composite Hurwitz series ring
idempotent element
PS-ring

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10.1080/00927872.2020.1721733

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title = "On a conjecture posed by Benhissi and Koja",

abstract = "Let (Formula presented.) = (Rn)n≥0 be an ascending chain of commutative rings with identity and (Formula presented.) (resp., (Formula presented.)) the generalized composite Hurwitz series ring (resp., generalized composite Hurwitz polynomial ring). In this paper, we completely characterize when the rings (Formula presented.) and (Formula presented.) are PS-rings. More precisely, we show that (Formula presented.) and (Formula presented.) are always PS-rings. This is an affirmative answer to the question raised by Benhissi and Koja. Communicated by Silvana Bazzoni.",

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AU - Lim, Jung Wook

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N2 - Let (Formula presented.) = (Rn)n≥0 be an ascending chain of commutative rings with identity and (Formula presented.) (resp., (Formula presented.)) the generalized composite Hurwitz series ring (resp., generalized composite Hurwitz polynomial ring). In this paper, we completely characterize when the rings (Formula presented.) and (Formula presented.) are PS-rings. More precisely, we show that (Formula presented.) and (Formula presented.) are always PS-rings. This is an affirmative answer to the question raised by Benhissi and Koja. Communicated by Silvana Bazzoni.

AB - Let (Formula presented.) = (Rn)n≥0 be an ascending chain of commutative rings with identity and (Formula presented.) (resp., (Formula presented.)) the generalized composite Hurwitz series ring (resp., generalized composite Hurwitz polynomial ring). In this paper, we completely characterize when the rings (Formula presented.) and (Formula presented.) are PS-rings. More precisely, we show that (Formula presented.) and (Formula presented.) are always PS-rings. This is an affirmative answer to the question raised by Benhissi and Koja. Communicated by Silvana Bazzoni.

KW - Annihilator

KW - generalized composite Hurwitz polynomial ring

KW - generalized composite Hurwitz series ring

KW - idempotent element

KW - PS-ring

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SP - 2655

EP - 2661

JO - Communications in Algebra

JF - Communications in Algebra

IS - 6

ER -

On a conjecture posed by Benhissi and Koja

Abstract

Keywords

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