A Generalization of Epiform Modules

Payman M. Hamaali
2014 Journal of Zankoy Sulaimani - Part A  
Let U be a family of R-modules and V be a submodule of a direct sum of some elements in U. The aim of this paper is to generalize basis and free modules. We use the concept of U v-generated module and X-sublinearly independent to provide the definition of U-basis and U-free module. We construct a U -basis of an R-module M as a pair (X, V), which a family U is X-sub-linearly independent to M and M is a Uv-generated module. Furthermore, we define Ubasis of M as a U -basis which has the maximal
more » ... has the maximal element on the first component and the minimal element on the second component of a pair (X, V). The results show that the first component of (X, V) in U -basis is closed under submodules and intersections. Moreover, we prove that the second component of (X, V) in U -basis is closed under direct sums. We also determine some U -free modules related to a family U which contains all Z-module Z modulo p power of n, where p prime and n ≥ 2.
doi:10.17656/jzs.10287 fatcat:zgv6s4yc5bbyrg6vhcoc7yv7ma