INTEGRAL CLOSURE AND OTHER OPERATIONS ON MONOMIAL IDEALS

INTEGRAL CLOSURE AND OTHER OPERATIONS ON MONOMIAL IDEALS

In this paper we give a characterization of integrally closed monomial ideals in two variables. The notion of x- and y-tight ideals is introduced. We also present a monomial version of a result of Watanabe on chains of integrally closed monomial ideals. Using the developed techniques, we prove resul...

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Veröffentlicht in:Journal of commutative algebra 2010, Vol.2 (3), p.359-386
1. Verfasser: QUIÑONEZ, VERONICA CRISPIN
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Business orders
Commutativity
Factorization
Integers
Mathematical integrals
Mathematical rings
Polynomials
Staircases
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Zusammenfassung:In this paper we give a characterization of integrally closed monomial ideals in two variables. The notion of x- and y-tight ideals is introduced. We also present a monomial version of a result of Watanabe on chains of integrally closed monomial ideals. Using the developed techniques, we prove results about the quadratic transforms and products in classes of monomial ideals, and describe multiplication in two classes of ideals in an integral domain.
ISSN:1939-0807
1939-2346
1939-2346
DOI:10.1216/JCA-2010-2-3-359