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2005•Communications in AlgebraRequires access

*-SIMPLE COMPLETE MONOMIAL IDEALS

John F. Gately

Open publisher page 10 citations

Abstract

Let R := k[x1, x2, x3] be a 3-dimensional polynomial ring over a field k. We prove that a (x1, x2, x3)-primary monomial ideal in such a ring is *-simple if it has minimal multiplicity with respect to each of its fibers. We also survey the known classes of *-simple monomial ideals in rings of this type and show that this new class is distinct from other known classes.

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What this paper is about

Let R := k[x1, x2, x3] be a 3-dimensional polynomial ring over a field k. We prove that a (x1, x2, x3)-primary monomial ideal in such a ring is *-simple if it has minimal multiplicity with respect to each of its fibers. We also survey the known classes of *-simple monomial ideals in rings of this type and show that this new class is distinct from other known classes.

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OpenAlex reports 10 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Let R := k[x1, x2, x3] be a 3-dimensional polynomial ring over a field k. We prove that a (x1, x2, x3)-primary monomial ideal in such a ring is *-simple if it has minimal multiplicity with respect to each of its fibers. We also survey the known classes of *-simple monomial ideals in rings of this type and show that this new class is distinct from other known classes.

Key concepts: Monomial, Mathematics, Polynomial ring, Multiplicity (mathematics), Monomial ideal, Simple (philosophy), Monomial basis, Simple ring

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