Some Classes of Monomial Ideals with Linear Quotients - Rahmati-Asghar, Rahim
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Monomial ideals are at the intersection of commutative algebra and combinatorics. Many important problems in polynomial rings can be reduced to the study of monomial ideals. To squarefree monomial ideals, one may attach simplicial complexes and vice versa. Namely, with any simplicial complex one may associate a squarefree monomial ideal, generated by the squarefree monomials corresponding to the minimal non-faces of the simplicial complex. On one hand, this allows the study of simplicial complexes by algebraic methods.

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Produktbeschreibung
Monomial ideals are at the intersection of commutative algebra and combinatorics. Many important problems in polynomial rings can be reduced to the study of monomial ideals. To squarefree monomial ideals, one may attach simplicial complexes and vice versa. Namely, with any simplicial complex one may associate a squarefree monomial ideal, generated by the squarefree monomials corresponding to the minimal non-faces of the simplicial complex. On one hand, this allows the study of simplicial complexes by algebraic methods.
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Autorenporträt
Dr. Rahim Rahmati-Asghar has obtained his PhD degree in Commutative Algebra in 2012. Now he is an assistant professor at the University of Maragheh. He is the author of several articles in Combinatorial Commutative Algebra, Algebraic Geometry and Combinatorics.