Abstract
In the present paper, t-generalized supplemented modules are defined starting from the generalized ⨁-supplemented modules. In addition, we present examples separating the t-generalized supplemented modules, supplemented modules, and generalized ⨁-supplemented modules and also show the equality of these modules for projective and finitely generated modules. Moreover, we define cofinitely t-generalized supplemented modules and give the characterization of these modules. Furthermore, for any ring R, we show that any finite direct sum of t-generalized supplemented R-modules is t-generalized supplemented and that any direct sum of cofinitely t-generalized supplemented R-modules is a cofinitely t-generalized supplemented module.
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