Composite hurwitz rings as PF-rings and PP-rings

Dong Kyu Kim; Jung Wook Lim

doi:10.3390/math8010100

Composite hurwitz rings as PF-rings and PP-rings

Dong Kyu Kim, Jung Wook Lim

Kyungpook National University

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

1 Scopus citations

Abstract

Let R ⊆ T be an extension of commutative rings with identity and H(R, T) (respectively, h(R, T) the composite Hurwitz series ring (respectively, composite Hurwitz polynomial ring). In this article, we study equivalent conditions for the rings H(R, T) and h(R, T) to be PF-rings and PP-rings. We also give some examples of PP-rings and PF-rings via the rings H(R, T) and h(R, T).

Original language	English
Article number	100
Journal	Mathematics
Volume	8
Issue number	1
DOIs	https://doi.org/10.3390/math8010100
State	Published - 1 Jan 2020

Keywords

Annihilator
Composite Hurwitz polynomial ring
Composite Hurwitz series ring
Idempotent element
McCoy condition
PF-ring
PP-ring
Torsion-free Z-module

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10.3390/math8010100

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title = "Composite hurwitz rings as PF-rings and PP-rings",

abstract = "Let R ⊆ T be an extension of commutative rings with identity and H(R, T) (respectively, h(R, T) the composite Hurwitz series ring (respectively, composite Hurwitz polynomial ring). In this article, we study equivalent conditions for the rings H(R, T) and h(R, T) to be PF-rings and PP-rings. We also give some examples of PP-rings and PF-rings via the rings H(R, T) and h(R, T).",

keywords = "Annihilator, Composite Hurwitz polynomial ring, Composite Hurwitz series ring, Idempotent element, McCoy condition, PF-ring, PP-ring, Torsion-free Z-module",

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T1 - Composite hurwitz rings as PF-rings and PP-rings

AU - Kim, Dong Kyu

AU - Lim, Jung Wook

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N2 - Let R ⊆ T be an extension of commutative rings with identity and H(R, T) (respectively, h(R, T) the composite Hurwitz series ring (respectively, composite Hurwitz polynomial ring). In this article, we study equivalent conditions for the rings H(R, T) and h(R, T) to be PF-rings and PP-rings. We also give some examples of PP-rings and PF-rings via the rings H(R, T) and h(R, T).

AB - Let R ⊆ T be an extension of commutative rings with identity and H(R, T) (respectively, h(R, T) the composite Hurwitz series ring (respectively, composite Hurwitz polynomial ring). In this article, we study equivalent conditions for the rings H(R, T) and h(R, T) to be PF-rings and PP-rings. We also give some examples of PP-rings and PF-rings via the rings H(R, T) and h(R, T).

KW - Annihilator

KW - Composite Hurwitz polynomial ring

KW - Composite Hurwitz series ring

KW - Idempotent element

KW - McCoy condition

KW - PF-ring

KW - PP-ring

KW - Torsion-free Z-module

UR - http://www.scopus.com/inward/record.url?scp=85080114887&partnerID=8YFLogxK

U2 - 10.3390/math8010100

DO - 10.3390/math8010100

M3 - Article

AN - SCOPUS:85080114887

SN - 2227-7390

VL - 8

JO - Mathematics

JF - Mathematics

IS - 1

M1 - 100

ER -

Composite hurwitz rings as PF-rings and PP-rings

Abstract

Keywords

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