In this paper we consider five possible extensions of the Prufer domain notion to the case of commutative rings with zero divisors and relate the corresponding properties on a ring with the property of its total ring of quotients. We show that a Prufer ring R satisfies one of the five conditions if and only if the total ring of quotients Q(R) of R satisfies that same condition. We focus in particular on the Gaussian property of a ring

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We prove that every tilting module of projective dimension at most one is of finite type, namely that its associated tilting class is the Ext-orthogonal of a family of finitely presented modules of projective dimension at most one.

Ž .The class semigroup of a commutative integral domain R is the semigroup S S R of the isomorphism classes of the nonzero ideals of R with operation induced by Ž . multiplication. A domain R is said to be Clifford regular if S S R is a Clifford Ž . semigroup, i.e. S S R is the disjoint union of the subgroups associated to the idempotent elements. In this paper we characterize the noetherian and the integrally closed Clifford regular domains and find some properties of an arbitrary Clifford regular domain. ᮊ

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