Full Ideals

Hong, Jooyoun; Lee, Heisook; Noh, Sunsook; Rush, David E.

doi:10.1080/00927870902747340

Cited by 9 publications

(7 citation statements)

References 10 publications

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“…Weakly m-full ideals are also called basically full in [7] and weakly m-full in [4]. See [3,4,5,6,7,9,14,15,16] and the references therein for more details.…”

Section: Applicationsmentioning

confidence: 99%

On colon operations and special types of ideals

Dao

2020

Preprint

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“…Weakly m-full ideals are also called basically full in [7] and weakly m-full in [4]. See [3,4,5,6,7,9,14,15,16] and the references therein for more details.…”

Section: Applicationsmentioning

confidence: 99%

On colon operations and special types of ideals

Dao

2020

Preprint

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“…Definition 1 ([10], Definition 4). An ideal I of R is said to be m-full if there exists an element x in R such that mI : x = I. m-full ideals are studied in [2], [4], [5], [8], [10], [11] and [12].…”

Section: Some Properties Of M-full Idealsmentioning

confidence: 99%

The weak Lefschetz property for ${\mathfrak{m}}$-full ideals and componentwise linear ideals

Harima¹,

Watanabe²

2012

Illinois J. Math.

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We give a necessary and sufficient condition for a standard graded Artinian ring of the form K[x 1 , . . . , xn]/I, where I is an m-full ideal, to have the weak Lefschetz property in terms of graded Betti numbers. This is a generalization of a theorem of Wiebe for componentwise linear ideals. We also prove that the class of componentwise linear ideals and that of completely m-full ideals coincide in characteristic zero and in positive characteristic, with the assumption that Gin(I) w.r.t. the graded reverse lexicographic order is stable.

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“…In particular, Watanabe has shown the following for two-dimensional regular local rings: In both [6] and [9], ideals, I, satisfying item (d) in the above theorem have been called full. Another result pertaining to m-full parameter ideals in regular local rings of any dimension can be summed up in the following theorem.…”

Section: Introductionmentioning

confidence: 99%