The Related Research Of Ringel-Schmidmeier-Simson Equivalences And Singular Equivalences

Let(?)the Morita ring such that M(?)A N=0 and N(?)B M=0.We define the monomorphism category S(?-mod)to be the subcategory of A-mod consisting of(X,Y,f,g)such that f:M(?)A X? Y is a Morita B-map and g:N(?)B Y? X is a Morita A-map.We show that this monomorphism category is a resolving subcategory of A-mod if and only if MA and NB are projective module,and moreover,we provide a sufficient and necessary condition such that it is a Frobenius category.We also use the left perpendicular category of a cotilting ?-module,to describe S(?-mod),and show that this cotilting module yields the Ringel-Schmidmeier-Simson equivalence between S(?-mod)and its dual.We also investigate the recollement of S(?-mod).We obtain new classes of singular equivalences which are constructed from Gorenstein-projective modules.