TY - JOUR

T1 - On prime rings whose central closure is finitely generated

AU - Chebotar, M.

AU - Ke, W. F.

AU - Lee, P. H.

AU - Puczyłowski, E. R.

N1 - Funding Information:
We would like to thank the National Center of Theoretical Sciences, Taiwan, for the support in organizing short visits of the first and the fourth authors.
Publisher Copyright:
© 2017 Elsevier Inc.

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.

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U2 - 10.1016/j.jalgebra.2017.06.021

DO - 10.1016/j.jalgebra.2017.06.021

M3 - Article

AN - SCOPUS:85030451199

SN - 0021-8693

VL - 488

SP - 282

EP - 289

JO - Journal of Algebra

JF - Journal of Algebra

ER -