학술논문
m-PRIMARY m-FULL IDEALS
이용수 2
- 영문명
- 발행기관
- 충청수학회
- 저자명
- Tae Whan Woo
- 간행물 정보
- 『Journal of the Chungcheong Mathematical Society』Volume 26, No. 4, 799~809쪽, 전체 11쪽
- 주제분류
- 자연과학 > 자연과학일반
- 파일형태
- 발행일자
- 2013.11.30
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국문 초록
영문 초록
An ideal I of a local ring (R; m; k) is said to be m-full if there exists an element x 2 m such that Im : x = I. An ideal I
of a local ring R is said to have the Rees property if ¹(I) > ¹(J) for any ideal J containing I. We study properties of m-full ideals and we characterize m-primary m-full ideals in terms of the minimal number of generators of the ideals. In particular, for a m -primary ideal I of a 2-dimensional regular local ring (R; m; k), we will show
that the following conditions are equivalent.
1. I is m-full
2. I has the Rees property
3. ¹(I) = o(I) + 1
In this paper, let (R; m; k) be a commutative Noetherian local ring with in¯nite residue ¯eld k = R=m.
목차
1. Introduction
2. Properties of m-full ideals
3. m-full ideals in a 2-dimensional regular local ring
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