Let $R$ be a commutative ring with identity and $T(R)$ its total quotientring. We extend the notion of well-centered overring of an integral domain toan arbitrary commutative ring and we investigate the transfer of this propertyto different extensions of commutative rings in both integral and non-integralcases. Namely in pullbacks and trivial extensions. Our aim is to provide newclasses of commutative rings satisfying this property and to shed light on someopen questions raised by Heinzer and Roitman in \cite{HR}.
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机译：假设$ R $是一个具有身份的交换环，而$ T（R）$是其总商数。我们将积分域的以中心为中心的Overring的概念扩展到任意交换环，并且我们研究了在整数和非整数情况下，该性质向交换环的不同扩展的转移。即在回调和琐碎的扩展中。我们的目的是提供满足该性质的新型交换环，并阐明Heinzer和Roitman在\ cite {HR}中提出的一些未解决的问题。
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