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On the Stanley depth of powers of some classes of monomial ideals. (English) Zbl 1409.13024

Summary: Given arbitrary monomial ideals \(I\) and \(J\) in polynomial rings \(A\) and \(B\) over a field \(K\), we investigate the Stanley depth of powers of the sum \(I+J\), and their quotient rings, in \(A\otimes_K B\) in terms of those of \(I\) and \(J\). Our results can be used to study the asymptotic behavior of the Stanley depth of powers of a monomial ideal. We tackle the case when \(J\) is a monomial complete intersection.

MSC:

13C15 Dimension theory, depth, related commutative rings (catenary, etc.)
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
13F20 Polynomial rings and ideals; rings of integer-valued polynomials

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References:

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