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We provide a framework connecting several well known theories related to thelinearity of graded modules over graded algebras. In the first part, we pay aparticular attention to the tensor products of graded bimodules over gradedalgebras. Finally, we provide a tool to evaluate the possible degrees of amodule appearing in a graded projective resolution once the generating degreesfor the first term of some particular projective resolution are known.

Generating degrees for graded projective resolutions