Valuation ideals and primary <i>w</i>-ideals

doi:10.1007/s11464-016-0554-7

Front. Math. China

2016, Vol. 11

Issue (4) : 829-844 https://doi.org/10.1007/s11464-016-0554-7

RESEARCH ARTICLE

Valuation ideals and primary w-ideals

Gyu Whan CHANG^1,²,Hwankoo KIM^1,^2,^*(

)

¹. Department of Mathematics Education, Incheon National University, Incheon 406-772, Republic of Korea
². Department of Information Security, Hoseo University, Asan 336-795, Republic of Korea

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Abstract

Let D be an integral domain, V(D) (resp., t-V(D)) be the set of all valuation (resp., t-valuation) ideals of D, and w-P(D) be the set of primary w-ideals of D. Let D[X] be the polynomial ring over D, c(f) be the ideal of D generated by the coefficients of f ∈ D[X], and N_v= {f ∈ D[X] | c(f)_v=D}. In this paper, we study integral domains D in which w-P(D) ⊆ t-V(D), t-V(D) ⊆ w-P(D), or t-V(D) = w-P(D). We also study the relationship between t-V(D) and V(D[X]Nv), and characterize when t-V(A + XB[X]) ⊆w-P(A + XB[X]) holds for a proper extension A ⊂ B of integral domains.

Keywords t-Valuation ideal primary w-ideal PvMD UMT-domain D[X]_Nv

Corresponding Author(s): Hwankoo KIM

Issue Date: 30 August 2016

Cite this article:

Gyu Whan CHANG,Hwankoo KIM. Valuation ideals and primary w-ideals[J]. Front. Math. China, 2016, 11(4): 829-844.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0554-7
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I4/829

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