On nil subsemigroups of rings with group identities

K. I. Beidar; Wen Fong Ke; Chia Hsin Liu

doi:10.1081/AGB-120006495

On nil subsemigroups of rings with group identities

K. I. Beidar^*, Wen Fong Ke, Chia Hsin Liu

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

Let R be a unital ring satisfying a group identity. We prove that if B is a nil subsemigroup of R, then it is locally nilpotent, and B^d is contained in the sum of all nilpotent ideals of R, where the positive integer d is determined by the group identity. Note that the above result for PI-rings is due to Amitsur.

Original language	English
Pages (from-to)	347-352
Number of pages	6
Journal	Communications in Algebra
Volume	30
Issue number	1
DOIs	https://doi.org/10.1081/AGB-120006495
Publication status	Published - 2002 Jan
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1081/AGB-120006495

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title = "On nil subsemigroups of rings with group identities",

abstract = "Let R be a unital ring satisfying a group identity. We prove that if B is a nil subsemigroup of R, then it is locally nilpotent, and Bd is contained in the sum of all nilpotent ideals of R, where the positive integer d is determined by the group identity. Note that the above result for PI-rings is due to Amitsur.",

author = "Beidar, {K. I.} and Ke, {Wen Fong} and Liu, {Chia Hsin}",

year = "2002",

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doi = "10.1081/AGB-120006495",

language = "English",

volume = "30",

pages = "347--352",

journal = "Communications in Algebra",

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TY - JOUR

T1 - On nil subsemigroups of rings with group identities

AU - Beidar, K. I.

AU - Ke, Wen Fong

AU - Liu, Chia Hsin

PY - 2002/1

Y1 - 2002/1

N2 - Let R be a unital ring satisfying a group identity. We prove that if B is a nil subsemigroup of R, then it is locally nilpotent, and Bd is contained in the sum of all nilpotent ideals of R, where the positive integer d is determined by the group identity. Note that the above result for PI-rings is due to Amitsur.

AB - Let R be a unital ring satisfying a group identity. We prove that if B is a nil subsemigroup of R, then it is locally nilpotent, and Bd is contained in the sum of all nilpotent ideals of R, where the positive integer d is determined by the group identity. Note that the above result for PI-rings is due to Amitsur.

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U2 - 10.1081/AGB-120006495

DO - 10.1081/AGB-120006495

M3 - Article

AN - SCOPUS:0036003478

SN - 0092-7872

VL - 30

SP - 347

EP - 352

JO - Communications in Algebra

JF - Communications in Algebra

IS - 1

ER -

On nil subsemigroups of rings with group identities

Abstract

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