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Stanley decompositions, pretty clean filtrations and reductions modulo regular elements. (English) Zbl 1155.13311

Summary: We study the behavior of Stanley decompositions and of pretty clean filtrations under reduction modulo a regular element.

MSC:

13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
13C14 Cohen-Macaulay modules
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
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