Abstract
Let \(\mathbb k\) be a field, and M and N two finitely generated graded modules over standard graded \(\mathbb k\)-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 \(A\otimes_{\mathbb k} B\)-module \(M\otimes_{\mathbb k} N\) 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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Sabzrou, H., Tousi, M. & Yassemi, S. Simplicial join via tensor product. manuscripta math. 126, 255–272 (2008). https://doi.org/10.1007/s00229-008-0175-x
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DOI: https://doi.org/10.1007/s00229-008-0175-x