On Armendariz-like properties in amalgamated algebras along ideals

Najib Mahdou; Abdeslam Mimouni; Mounir El Ouarrachi

doi:10.3906/mat-1603-135

On Armendariz-like properties in amalgamated algebras along ideals

Najib Mahdou, Abdeslam Mimouni^*, Mounir El Ouarrachi

^*Corresponding author for this work

Department of Mathematics

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

4 Scopus citations

Abstract

Let f: A → B be a ring homomorphism and J be an ideal of B. In this paper, we investigate the transfer of Armendariz-like properties to the amalgamation of A with B along J with respect to f (denoted by A ^f J) introduced and studied by D'Anna, Finocchiaro, and Fontana in 2009. Our aim is to provide necessary and sufficient conditions for A ^f J to be an Armendariz ring, nil-Armendariz ring, and weak Armendariz ring.

Original language	English
Pages (from-to)	1673-1686
Number of pages	14
Journal	Turkish Journal of Mathematics
Volume	41
Issue number	6
DOIs	https://doi.org/10.3906/mat-1603-135
State	Published - 2017

Bibliographical note

Publisher Copyright:
© TÜBI˙TAK.

Keywords

Amalgamated algebra along an ideal
Armendariz ring
Nil-Armendariz ring
Reduced ring
Semicommutative ring
Weak Armen-dariz

ASJC Scopus subject areas

General Mathematics

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10.3906/mat-1603-135

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title = "On Armendariz-like properties in amalgamated algebras along ideals",

abstract = "Let f: A → B be a ring homomorphism and J be an ideal of B. In this paper, we investigate the transfer of Armendariz-like properties to the amalgamation of A with B along J with respect to f (denoted by A f J) introduced and studied by D'Anna, Finocchiaro, and Fontana in 2009. Our aim is to provide necessary and sufficient conditions for A f J to be an Armendariz ring, nil-Armendariz ring, and weak Armendariz ring.",

keywords = "Amalgamated algebra along an ideal, Armendariz ring, Nil-Armendariz ring, Reduced ring, Semicommutative ring, Weak Armen-dariz",

author = "Najib Mahdou and Abdeslam Mimouni and \{El Ouarrachi\}, Mounir",

note = "Publisher Copyright: {\textcopyright} T{\"U}BI˙TAK.",

year = "2017",

doi = "10.3906/mat-1603-135",

language = "English",

volume = "41",

pages = "1673--1686",

journal = "Turkish Journal of Mathematics",

issn = "1300-0098",

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T1 - On Armendariz-like properties in amalgamated algebras along ideals

AU - Mahdou, Najib

AU - Mimouni, Abdeslam

AU - El Ouarrachi, Mounir

N1 - Publisher Copyright: © TÜBI˙TAK.

PY - 2017

Y1 - 2017

N2 - Let f: A → B be a ring homomorphism and J be an ideal of B. In this paper, we investigate the transfer of Armendariz-like properties to the amalgamation of A with B along J with respect to f (denoted by A f J) introduced and studied by D'Anna, Finocchiaro, and Fontana in 2009. Our aim is to provide necessary and sufficient conditions for A f J to be an Armendariz ring, nil-Armendariz ring, and weak Armendariz ring.

AB - Let f: A → B be a ring homomorphism and J be an ideal of B. In this paper, we investigate the transfer of Armendariz-like properties to the amalgamation of A with B along J with respect to f (denoted by A f J) introduced and studied by D'Anna, Finocchiaro, and Fontana in 2009. Our aim is to provide necessary and sufficient conditions for A f J to be an Armendariz ring, nil-Armendariz ring, and weak Armendariz ring.

KW - Amalgamated algebra along an ideal

KW - Armendariz ring

KW - Nil-Armendariz ring

KW - Reduced ring

KW - Semicommutative ring

KW - Weak Armen-dariz

UR - https://www.scopus.com/pages/publications/85034755151

U2 - 10.3906/mat-1603-135

DO - 10.3906/mat-1603-135

M3 - Article

AN - SCOPUS:85034755151

SN - 1300-0098

VL - 41

SP - 1673

EP - 1686

JO - Turkish Journal of Mathematics

JF - Turkish Journal of Mathematics

IS - 6

ER -

On Armendariz-like properties in amalgamated algebras along ideals

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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