ON MODULES OVER COMMUTATIVE RINGS

Our main purpose is to extend several results of interest that have been proved for modules over integral domains to modules over arbitrary commutative rings R with identity. The classical ring of quotients Q of R will play the role of the field of quotients when zero-divisors are present. After discussing torsion-freeness and divisibility (Sections 2-3), we study Matlis-cotorsion modules and their roles in two category equivalences (Sections 4-5). These equivalences are established via the same functors as in the domain case, but instead of injective direct sums EDQ one has to take the full subcategory of Q-modules into consideration. Finally, we prove results on Matlis rings, i.e. on rings for which Q has projective dimension 1 (Theorem 6.4).