On prime rings whose central closure is finitely generated

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

doi:10.1016/j.jalgebra.2017.06.021

On prime rings whose central closure is finitely generated

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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,…,c_n], for some c₁,…,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
Pages (from-to)	282-289
Number of pages	8
Journal	Journal of Algebra
Volume	488
DOIs	https://doi.org/10.1016/j.jalgebra.2017.06.021
Publication status	Published - 2017 Oct 15

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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