نجمه دهقانی

An R-module M is called quasi-morphic if for any f ∈ End R (M), there exist g,h ∈ End R (M) such that Imf = Kerg and Kerf = Imh. In addi- tion, M R is said to be morphic whenever g = h in the above definition. The main objective of this paper is investigating quasi-morphic property for several classes of modules. First we obtain general properties of quasi-morphic modules via exact sequence approach. Moreover, we investigate conditions under which a finite length quasi-morphic module is morphic. As a result, we show that for uniserial finite length modules, the notions of morphic and quasi-morphic coin- cide. Over a principal ideal domain R, direct sums of cyclic modules which are (quasi-)morphic are characterized. Among applications of our results, nonsin- gular extending (quasi-)morphic modules are characterized completely. We also prove that over a commutative Noetherian domain R which is not a field, quasi- morphic nonsingular extending modules are precisely direct sums of copies of Q (the quotient field o