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

Access to Document

10.1016/0022-4049(88)90090-4

Cite this

@article{3b0d30145a9244fabf9091c15a09f339,

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.",

author = "Moshe Roitman",

year = "1988",

month = mar,

doi = "10.1016/0022-4049(88)90090-4",

language = "English",

volume = "51",

pages = "205--215",

journal = "Journal of Pure and Applied Algebra",

issn = "0022-4049",

publisher = "Elsevier",

number = "1-2",

}

TY - JOUR

T1 - On the lifting problem for homogeneous ideals in polynomial rings

AU - Roitman, Moshe

PY - 1988/3

Y1 - 1988/3

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=38249032855&partnerID=8YFLogxK

U2 - 10.1016/0022-4049(88)90090-4

DO - 10.1016/0022-4049(88)90090-4

M3 - Article

AN - SCOPUS:38249032855

SN - 0022-4049

VL - 51

SP - 205

EP - 215

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 1-2

ER -

On the lifting problem for homogeneous ideals in polynomial rings

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this