This paper investigates the projective dimension of the maximal right ring of quotients of a right non-singular ring R. Our discussion addresses the question under which conditions pd guarantees that the module is a direct sum of countably generated modules extending Matlis’ Theorem for integral domains to a non-commutative setting.
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Ulrich Albrecht, Bradley McQuaig, Divisibility and duo-rings. Rend. Sem. Mat. Univ. Padova 143 (2020), pp. 81–103DOI 10.4171/RSMUP/40