Simplicial join via tensor product

Abstract

Let be a field, and M and N two finitely generated graded modules over standard graded -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 ⊗B -module M ⊗ 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. © 2008 Springer-Verlag.