On direct limits of finite products of fields as subrings of a commutative ring (Q2809248)

\textit{R. Gilmer} and \textit{W. Heinzer} asked the question in [Trans. Am. Math. Soc. 331, No. 2, 663--680 (1992; Zbl 0760.13005)] which seems to have inspired the research: which zero-dimensional rings can be expressed as a direct limit of Artinian subrings. The paper focuses on answering the question, for a commutative ring \(R\) with Krull dimension zero, under what conditions does \(R\) admit direct limits of finite products of fields as subrings.NEWLINENEWLINEThe article is quite concise and begins by studying general properties on the existence of finite product of fields as a subring of a commutative ring. The author the proceeds to develop conditions under which a von Neumann regular ring contains a direct limit of finite product of fields. Along the way, there are several nice examples given to help illustrate the theorems as well as showing that converses do not hold.