Abstract
The homological degree is a cohomological degree generalizing the classical degree function of a module. Given a finitely generated graded module M, over a standard graded ring A, this note is concerned with the question of when, for an element x in the augmentation ideal of A that is not in any associated prime of M other than the augmentation ideal itself, the homological degree of M is equal to the homological degree of M/xM. This question is answered when the dimension of M is one or two.
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