Weak Silting Modules And Weak N-tilting Modules Over Morita Context Rings

In this paper,we study weak silting modules,silting modules and weak n-tilting modules over Morita context ring with zero bimodule homomorphisms.Let Λ(0,0)=(?)be a Morita context ring with zero bimodule homomorphisms,where A and B are rings,N is an A-B-bimodule,M is a B-A-bimodule.Let X be a right A-module and Y a right B-module.We mainly prove that a right Λ(0,0)module TA(X)⊕TB(Y)is weak silting if and only if both XA and YB are weak silting,HomB(M,Y+)∈ Cogen(X+),HomA(N,X+)∈ Cogen(Y+).We give that TA(X)⊕ TB(Y)is silting if and only if both XA and YB are silting,Y(?)BM ∈Gen(X),X (?)A N∈ Gen(Y).Moreover,if both BM and AN are flat,then we show that TA(X)⊕ TB(Y)is weak n-tilting if and only if both XA and YB are weak n-tilting,HomB(M,Y+)∈ Cogenn(X+),HomA(N,X+)∈ Cogenn(Y+).