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

Access to Document

10.1081/AGB-120006495

Cite this

@article{0003273780f84968a662bc4a06e62f83,

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",

month = jan,

doi = "10.1081/AGB-120006495",

language = "English",

volume = "30",

pages = "347--352",

journal = "Communications in Algebra",

issn = "0092-7872",

publisher = "Taylor and Francis Ltd.",

number = "1",

}

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.

UR - https://www.scopus.com/pages/publications/0036003478

UR - https://www.scopus.com/pages/publications/0036003478#tab=citedBy

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

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this