### 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[c_{1},…,c_{n}], for some c_{1},…,c_{n}∈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 |
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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

### Cite this

*Journal of Algebra*,

*488*, 282-289. https://doi.org/10.1016/j.jalgebra.2017.06.021

}

*Journal of Algebra*, vol. 488, pp. 282-289. https://doi.org/10.1016/j.jalgebra.2017.06.021

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

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 -