On prime rings whose central closure is finitely generated

M. Chebotar, Wen-Fong Ke, P. H. Lee, E. R. Puczyłowski

Research output: Contribution to journalArticle

Abstract

The purpose of the paper is to study prime rings R such that the central closure RC is a simple ring with 1 and it is finitely generated over R by elements of the extended centroid C, that is, RC=R[c1,…,cn], for some c1,…,cn∈C. In particular, we will show that if there exists a prime ring with zero center whose central closure is simple with 1 and generated by finitely many central elements, then there exists such a ring whose central closure is generated by two central elements.

Original languageEnglish
Pages (from-to)282-289
Number of pages8
JournalJournal of Algebra
Volume488
DOIs
Publication statusPublished - 2017 Oct 15

Fingerprint

Prime Ring
Finitely Generated
Central Element
Closure
Extended Centroid
Ring
Zero

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Chebotar, M. ; Ke, Wen-Fong ; Lee, P. H. ; Puczyłowski, E. R. / On prime rings whose central closure is finitely generated. In: Journal of Algebra. 2017 ; Vol. 488. pp. 282-289.
@article{1704e33fbf374b2cbdb5e1dbcced61be,
title = "On prime rings whose central closure is finitely generated",
abstract = "The purpose of the paper is to study prime rings R such that the central closure RC is a simple ring with 1 and it is finitely generated over R by elements of the extended centroid C, that is, RC=R[c1,…,cn], for some c1,…,cn∈C. In particular, we will show that if there exists a prime ring with zero center whose central closure is simple with 1 and generated by finitely many central elements, then there exists such a ring whose central closure is generated by two central elements.",
author = "M. Chebotar and Wen-Fong Ke and Lee, {P. H.} and Puczyłowski, {E. R.}",
year = "2017",
month = "10",
day = "15",
doi = "10.1016/j.jalgebra.2017.06.021",
language = "English",
volume = "488",
pages = "282--289",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",

}

On prime rings whose central closure is finitely generated. / Chebotar, M.; Ke, Wen-Fong; Lee, P. H.; Puczyłowski, E. R.

In: Journal of Algebra, Vol. 488, 15.10.2017, p. 282-289.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On prime rings whose central closure is finitely generated

AU - Chebotar, M.

AU - Ke, Wen-Fong

AU - Lee, P. H.

AU - Puczyłowski, E. R.

PY - 2017/10/15

Y1 - 2017/10/15

N2 - The purpose of the paper is to study prime rings R such that the central closure RC is a simple ring with 1 and it is finitely generated over R by elements of the extended centroid C, that is, RC=R[c1,…,cn], for some c1,…,cn∈C. In particular, we will show that if there exists a prime ring with zero center whose central closure is simple with 1 and generated by finitely many central elements, then there exists such a ring whose central closure is generated by two central elements.

AB - The purpose of the paper is to study prime rings R such that the central closure RC is a simple ring with 1 and it is finitely generated over R by elements of the extended centroid C, that is, RC=R[c1,…,cn], for some c1,…,cn∈C. In particular, we will show that if there exists a prime ring with zero center whose central closure is simple with 1 and generated by finitely many central elements, then there exists such a ring whose central closure is generated by two central elements.

UR - http://www.scopus.com/inward/record.url?scp=85030451199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030451199&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2017.06.021

DO - 10.1016/j.jalgebra.2017.06.021

M3 - Article

AN - SCOPUS:85030451199

VL - 488

SP - 282

EP - 289

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -