Centers of regular self-injective rings (Q5917630)

The interesting result shown in this paper is that the center of any factor ring of a von Neumann regular right self-injective ring \(R\) is a factor ring of the center of \(R\), which unifies both Theorem 3.6 in [\textit{K. R. Goodearl}, Pac. J. Math. 76, 381-395 (1978; Zbl 0351.16007)] and Corollary 3.3 in [\textit{A. Rosenberg}, Ann. Math., II. Ser. 68, 278-294 (1958; Zbl 0128.255)]. Furthermore as a corollary, it is proved that the center of the maximal right quotient ring of any prime factor ring \(R\) of a von Neumann regular right continuous ring is equal to the center of \(R\), which extends Corollary 2.4 in [\textit{P. Ara}, Arch. Math. 50, 342- 347 (1988; Zbl 0661.16001)]. Also some interesting examples related to these results are provided.