We show that there is a reflection type bijection between the indecomposable summands of two multiplicity free tilting modules X and Y. This fixes common Y sends projective (resp., injective) exactly one module to non-projective non-injective) other. Moreover, this interchanges possible non-isomorphic complements an almost complete module.

This work is devoted to give a charcaterization of a pomonoid $S$ such that all cyclic $S$-posets are regular injective.

Let R be a right GF-closed ring with finite left and right Gorenstein global dimension. We prove that if I is an ideal of R such that R/I is a semi-simple ring, then the Gorensntein flat dimensnion of R/I as a right R-module and the Gorensntein injective dimensnnion of R/I as a left R-module are identical. In particular, we show that for a simple module S over a commutative Gorensntein ring R, ...