Strongly m-full modules

Abstract

We introduce the stongly m - full property for a pair of graded modules, which is stronger than the m - full property but weaker than the componentwise m - full property, and give criteria for strong m - fullness by means of strongly m - full closure. One more property for a pair of graded modules : the m - adic m - fullness is introduced. Using strongly m - full closure , we show that m - adic m - fullness and componentwise m - fullness are equivalent.