In this article we present a new class of modules which is named as principally -lifting modules. This termed by Principally in work defined as, module called if for every cyclic submodule with , there decomposition such that and g-small . Thus, ring it -module. We determined structure. Several characterizations, properties, instances are described these modules'.

A square matrix is principally unimodular if every principal submatrix has determinant 0 or 1. Let A be a symmetric (0; 1)-matrix, with a zero diagonal. A PU-orientation of A is a skew-symmetric signing of A that is PU. If A 0 is a PU-orientation of A, then, by a certain decomposition of A, we can construct every PU-orientation of A from A 0. This construction is based on the fact that the PU-o...