Rees property and its related properties of modules

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Properties of ideals of a commutative Noetherian local ring or a Noetherian standerd graded commutative algebra over a field, called the Rees property, the second Rees property, the m-fullness and the fullness, can naturally be extended to the properties of modules. We introduce the property of modules called “weak” m-fullness and “weak” fullness. We show that the Rees property and the m-fullness are equivalent in the class of modules with weak m-fullness, and also that the second Rees property and the fullness are equivalent in the class of modules with weak fullness.

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