In this paper we show that a ring R is von Neumann regular (or a V-ring) if and only if every central localization of R at a maximal ideal of its center is von Neumann regular (or a V-ring). Strongly regular rings are characterized by the property that all central localizations at maximal ideals of the center are division rings. Also we consider whether regular PI-rings can be characterized by the property that all central localizations at maximal ideals of the center are simple. Commutative von Neumann regular rings have been characterized in various ways. However, very few of these characterizations extend to noncommutative rings. The results in this paper arose from attempting to extend to noncommutative rings a well-known theorem of Kaplansky [11, Theorem 6] which states that commutative regular rings are characterized by the property that all localizations at maximal ideals are fields. It turns out that the obvious extension of this theorem to the noncommutative case is valid. That being, a ring is regular if and only. if all central localizations at maximal ideals of the center are regular. An analogous theorem is obtained for Vrings. Also we show that strongly regular rings are characterized by the property that all central localizations at maximal ideals of the center are division rings. With an eye to the commutative theory, we consider whether regular PIrings can be characterized by the property that all central localizations at maximal ideals of the center are simple. We provide an example to show that this is not the case. However, it is true if and only if contraction provides a 1:1 correspondence between maximal ideals of the ring and maximal ideals
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