Finite filtrations of modules and shellable multicomplexes

By Jürgen Herzog, Dorin Vicentiu Popescu. 2005

99 citations recorded by the source corpus.

We introduce pretty clean modules, extending the notion of clean modules by Dress, and show that pretty clean modules are sequentially Cohen–Macaulay. We also extend a theorem of Dress on shellable simplicial complexes to multicomplexes.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/661a8e2b30894a4a01dd5f71ee8ca9eae0ed99a6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Asia Rauf
2. Jürgen Herzog
3. Xinxian Zheng
4. Marius Vladoiu
5. Ali Soleyman Jahan
6. Adam Van Tuyl
7. Huy Tài Hà
8. Rafael H. Villarreal

In Computational Theory and Mathematics

1. Asia Rauf
2. Jürgen Herzog
3. Marius Vladoiu
4. Xinxian Zheng
5. Ali Soleyman Jahan
6. Adam Van Tuyl
7. Huy Tài Hà
8. Rafael H. Villarreal

In Geometry and Topology

1. Asia Rauf
2. Jürgen Herzog
3. Marius Vladoiu
4. Xinxian Zheng
5. Ali Soleyman Jahan
6. Huy Tài Hà
7. Adam Van Tuyl
8. Susan Morey

Citations in the corpus

• Prime filtrations of monomial ideals and polarizations (2006, background): “Recall that the prime filtration F is called pretty clean, if for all i j which Pi ⊆ Pj it follows that Pi = Pj .”
• How to compute the Stanley depth of a monomial ideal (2007, methodology): “The conjecture is widely open (see however [1], [10], [11] and [1 4]).”
• STANLEY DECOMPOSITIONS, PRETTY CLEAN FILTRATIONS AND REDUCTIONS MODULO REGULAR ELEMENTS (2007, methodology): “Then by the isomorphism (2) we obtain the following Stanley decomposition”