Note on clear rings

A. Mimouni

doi:10.1007/s13370-022-00973-2

Note on clear rings

A. Mimouni^*

^*Corresponding author for this work

Department of Mathematics

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

Abstract

Let R be a commutative ring with identity. An element x∈ R is said to be a clear element if it can be written as x= a+ v where a is a unit-regular element, that is a= a²u for some u∈ U(R) and v∈ U(R) ; and the ring itself is said to be a clear ring provided that every element is a clear element. In this paper we study the notions of clear rings in different contexts of commutative rings such us pullbacks, trivial ring extensions, amalgamations of algebras along ideals etc.

Original language	English
Article number	49
Journal	Afrika Matematika
Volume	33
Issue number	2
DOIs	https://doi.org/10.1007/s13370-022-00973-2
State	Published - Jun 2022

Bibliographical note

Publisher Copyright:
© 2022, African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature.

Keywords

Amalgamation
Clear element
Clear ring
Pullbacks
Trivial ring extension

ASJC Scopus subject areas

General Mathematics

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10.1007/s13370-022-00973-2

Cite this

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title = "Note on clear rings",

abstract = "Let R be a commutative ring with identity. An element x∈ R is said to be a clear element if it can be written as x= a+ v where a is a unit-regular element, that is a= a2u for some u∈ U(R) and v∈ U(R) ; and the ring itself is said to be a clear ring provided that every element is a clear element. In this paper we study the notions of clear rings in different contexts of commutative rings such us pullbacks, trivial ring extensions, amalgamations of algebras along ideals etc.",

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doi = "10.1007/s13370-022-00973-2",

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AU - Mimouni, A.

PY - 2022/6

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N2 - Let R be a commutative ring with identity. An element x∈ R is said to be a clear element if it can be written as x= a+ v where a is a unit-regular element, that is a= a2u for some u∈ U(R) and v∈ U(R) ; and the ring itself is said to be a clear ring provided that every element is a clear element. In this paper we study the notions of clear rings in different contexts of commutative rings such us pullbacks, trivial ring extensions, amalgamations of algebras along ideals etc.

AB - Let R be a commutative ring with identity. An element x∈ R is said to be a clear element if it can be written as x= a+ v where a is a unit-regular element, that is a= a2u for some u∈ U(R) and v∈ U(R) ; and the ring itself is said to be a clear ring provided that every element is a clear element. In this paper we study the notions of clear rings in different contexts of commutative rings such us pullbacks, trivial ring extensions, amalgamations of algebras along ideals etc.

KW - Amalgamation

KW - Clear element

KW - Clear ring

KW - Pullbacks

KW - Trivial ring extension

UR - https://www.scopus.com/pages/publications/85127970028

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DO - 10.1007/s13370-022-00973-2

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SN - 1012-9405

VL - 33

JO - Afrika Matematika

JF - Afrika Matematika

IS - 2

M1 - 49

ER -

Note on clear rings

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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