LARGE MAXIMAL SECOND MODULES AND LARGE MAXIMAL SMALL SECOND MODULES

Abstract

The notions of large maximal second modules and large maximal small secondmodules are submitted as generalizations of essential second modules and small second mod-ules; respectively, where a T-module V is named a large maximal second module (simply LM second). If for a proper an ideal H of T, then either V H = (0) or V H < LM V and a T-module V is named a large maximal small second module (simply LMS second).Further, iffor a proper an ideal H of T, then either V H = (0) or V H < LMS V ,with a number of char-acteristics and some fundamental features and theorems of these concepts are given. Thisstudy also shows the relationship between these ideas and other types of second modules.