It is a classical result that if (Ä,3J!) is a complete discrete valuation ring with quotient field K, and if RjJil is perfect, then any finite dimensional central simple A"-aIgebra S can be split by a field L which is an unramified extension of K. Here we prove that if OR, 3JÎ) is any regular local ring, and if 2 contains an Ä-order A whose global dimension is finite and such that A/Rad A is central simple over /f/3Ji, then the existence of an "Ä-unramified" splitting field L for S implies that

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... A is Ä-separable. Using this theorem we construct an example which shows that if R is a regular local ring of dimension greater than one, and if its characteristic is not 2, then there is a central division algebra over K which has no Ä-unramified splitting field.