Abstract
In this paper, a new concept has been presented that is a stronger than a previous concept called -G--supplemented. The basic definition is in an ring where an -module is said to be principally -G--supplemented (shortly, -PG--supplemented) if any cyclic submodule of with , there exists a direct summand of such that and . A set of properties and relations between previous modules and the given module has been dealt with simple examples illustrating those relations.
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