Total Of Modules & Rings And Structure Of Relative Modules

In this dissertation, we describe some important properties of the total of modules & rings and the structure of relative modules. The character of the total of modules & rings and some examples are given; the classes of rings and modules with zero total are investigated; we build the decomposition theorems on some a.c.c. projective modules over radicaltotal rings; generalized inverse theories are applied on modules & rings and a equivalent condition of semisimple modules are given and we obtain a decomposition of torsionfree module Q over a domain R which satisfies w.dim Q = n<8 and ?(Q,M) = Tote(Q,M) for all torsionfree R-modules.