Given a hereditary torsion theory in Mod-, a module is called -supplemented if every submodule of contains a direct summand of with torsion. A submodule of is called -supplement of in if and and is -weakly supplemented if every submodule...
The purpose of this paper is to provide a criterion of an occurrence of uncountably generated uniserial modules over chain rings. As we show it suffices to investigate two extreme cases, nearly simple chain rings, i.e. chain rings containing only three two-sided ideals, and chain rings with “many” two-sided ideals. We prove that there exists an -generated uniserial module over every non-artinian nearly simple chain ring and over chain rings containing an uncountable strictly increasing (resp. decreasing)...