GENERALIZED COFINITELY SEMIPERFECT MODULES

Abstract

In the present paper, we define generalized (amply) cofinitely supplemented modules, and generalized circle plus-cofinitely supplemented modules are defined as a generalization of (amply) cofinitely supplemented modules and circle plus-cofinitely supplemented modules, respectively, and show, among others, the following results: (1) The class of generalized cofinitely supplemented modules is closed under taking homomorphic images, generalized covers and arbitrary direct sums. (2) Any finite direct sum of generalized circle plus-cofinitely supplemented modules is a generalized circle plus-cofinitely supplemented module. (3) M is a generalized cofinitely semiperfect module if and only if M is a generalized cofinitely supplemented - module by supplements which have generalized projective covers.