Abstract
The notion of Barbilian domain as introduced and studied by W. Leisner [14], [16] and others is refined here to n-Barbilian domain in a free module of rank n. This leads to results that bear on n-dimensional affine ring geometry. The case of infinite rank is also considered. AMS Classification: 51C05. Keywords: Free module, Barbilian domain, Hermite ring, affine ring geometry.
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