Strongly π-Rickart Modules And T-π-Rickart Modules

The concept of strongly π-Rickart modules is introduced in chapter 3.A mod-ule M is called strongly π-Rickart if for any f ∈ EndR(M),there exists a positive integer n such that rM(fn)is a fully invariant direct summand of M.Its basic prop-erties are studied and the relationships among strongly π-Rickart modules,strongly Rickart modules and π-Rickart modules are investigated.In addition,it is proved that any direct summand of strongly π-Rickart modules is also strongly π-Rickart.The concept of t-π-Rickart modules is introduced and its properties are studied in chapter 4.It is proven that every direct summand of a t-πRickart module inherits the property and if M is a t-π-Rickart module,then M = Z2(M)+ M’ with M’ is a(nonsingular)π-Rickart module.