Resumen de Two-Sided Essential Submodules of Q(R)

Albrecht Ulrich

• The focus of this paper are essential submodules A of the maximal right ring of quotients, Q(R), of a right non-singular ring R. Since Q(R) is a R-R-bimodule, particular attention is given to submodules of the right R-module Q(R) which are also submodules of the left R-module Q(R). In this discussion, properties of R which are inherited by intermediate rings S contained between R and Q(R) are investigated. The results obtained are used to discuss homological properties of essential submodules A of Q(R). In particular, the paper addresses the question when S-closed submodules of finite direct sums of copies of A are direct summands.