Group identities and prime rings generated by units

Tsiu Kwen Lee; Chia Hsin Liu

doi:10.1081/AGB-120022227

Group identities and prime rings generated by units

Tsiu Kwen Lee, Chia Hsin Liu^*

^*Corresponding author for this work

Department of Mathematics

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

3 Citations (Scopus)

Abstract

Let R be a prime ring and U(R) the group of units of R. We prove that if U(R) generates R and satisfies a group identity, then R is either a domain or a full matrix ring over a finite field.

Original language	English
Pages (from-to)	3305-3309
Number of pages	5
Journal	Communications in Algebra
Volume	31
Issue number	7
DOIs	https://doi.org/10.1081/AGB-120022227
Publication status	Published - 2003 Jul

Keywords

Generalized polynomial identities
Group identities
Prime rings
Units

ASJC Scopus subject areas

Algebra and Number Theory

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10.1081/AGB-120022227

Cite this

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title = "Group identities and prime rings generated by units",

abstract = "Let R be a prime ring and U(R) the group of units of R. We prove that if U(R) generates R and satisfies a group identity, then R is either a domain or a full matrix ring over a finite field.",

keywords = "Generalized polynomial identities, Group identities, Prime rings, Units",

author = "Lee, {Tsiu Kwen} and Liu, {Chia Hsin}",

note = "Funding Information: The work was partially supported by NSC. The second author thanks National Sun Yat-sen University. Part of the research was done there.",

year = "2003",

month = jul,

doi = "10.1081/AGB-120022227",

language = "English",

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pages = "3305--3309",

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T1 - Group identities and prime rings generated by units

AU - Lee, Tsiu Kwen

AU - Liu, Chia Hsin

N1 - Funding Information: The work was partially supported by NSC. The second author thanks National Sun Yat-sen University. Part of the research was done there.

PY - 2003/7

Y1 - 2003/7

N2 - Let R be a prime ring and U(R) the group of units of R. We prove that if U(R) generates R and satisfies a group identity, then R is either a domain or a full matrix ring over a finite field.

AB - Let R be a prime ring and U(R) the group of units of R. We prove that if U(R) generates R and satisfies a group identity, then R is either a domain or a full matrix ring over a finite field.

KW - Generalized polynomial identities

KW - Group identities

KW - Prime rings

KW - Units

UR - http://www.scopus.com/inward/record.url?scp=0042473892&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042473892&partnerID=8YFLogxK

U2 - 10.1081/AGB-120022227

DO - 10.1081/AGB-120022227

M3 - Article

AN - SCOPUS:0042473892

SN - 0092-7872

VL - 31

SP - 3305

EP - 3309

JO - Communications in Algebra

JF - Communications in Algebra

IS - 7

ER -

Group identities and prime rings generated by units

Abstract

Keywords

ASJC Scopus subject areas

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