Long exact sequence of U-extension modules

Let R be commutative algebra with unit element. Given any R -modules M and N, and any nonzero submodule U of M, Mahatma and Muchtadi-Alamsyah defined the k -th U -extension module of N by M for every positive integer k. Further, Mahatma showed that given any short exact sequence of R -modules and R -module homomorphisms, there exists an exact sequence of U -extension modules of N by M. It is just that the sequence consists of only limited number of nonzero modules. In this paper we investigate the conditions needed by the sequence so that it can be extended into a longer one.