Let be a ring with unit element and let R -S{x, d} be the Ore-extension of with respect to a derivation d of S. Our object in this paper is to show that I. gl. dim R = 1 + l.gl. imS, if 5 is a commutative Noetherian ring and d is suitably restricted.
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Gopalakrishnan et al. (1966) studied this question.