On the lifting problem for homogeneous ideals in polynomial rings

Moshe Roitman

doi:10.1016/0022-4049(88)90090-4

On the lifting problem for homogeneous ideals in polynomial rings

Moshe Roitman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove here that if k is a field of zero characteristic, then any homogenous ideal in k[X, Y] is liftable to a radical ideal. On the other hand, if k is a finite field, then for any n ≥ 2, there exist zero-dimensional monomial ideals in k[X₁,...,X_n] which are not liftable to radical ideals.

Original language	English
Pages (from-to)	205-215
Number of pages	11
Journal	Journal of Pure and Applied Algebra
Volume	51
Issue number	1-2
DOIs	https://doi.org/10.1016/0022-4049(88)90090-4
State	Published - Mar 1988

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/0022-4049(88)90090-4

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title = "On the lifting problem for homogeneous ideals in polynomial rings",

abstract = "We prove here that if k is a field of zero characteristic, then any homogenous ideal in k[X, Y] is liftable to a radical ideal. On the other hand, if k is a finite field, then for any n ≥ 2, there exist zero-dimensional monomial ideals in k[X1,...,Xn] which are not liftable to radical ideals.",

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AB - We prove here that if k is a field of zero characteristic, then any homogenous ideal in k[X, Y] is liftable to a radical ideal. On the other hand, if k is a finite field, then for any n ≥ 2, there exist zero-dimensional monomial ideals in k[X1,...,Xn] which are not liftable to radical ideals.

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On the lifting problem for homogeneous ideals in polynomial rings

Abstract

ASJC Scopus subject areas

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