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 language | English |
|---|---|
| Pages (from-to) | 282-289 |
| Number of pages | 8 |
| Journal | Journal of Algebra |
| Volume | 488 |
| DOIs | |
| Publication status | Published - 2017 Oct 15 |
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All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
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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 journal › Article
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 -