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|Paper IPM / M / 8832||
Let k be a field, and M and N two finitely generated graded modules over standard graded k-algebras A and B, respectively. We will study generalized, sequentially, almost, and approximately Cohen-Macaulay as well as clean, and pretty clean properties of the A⊗k B-module M⊗k N through the corresponding properties of M and N. The behavior of these properties with respect to the simplicial join of two simplicial (multi)complexes will be revealed as corollaries.
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