[1]周德川,王芳贵,胡 葵.Kronecker函数环对PvMD的一个新刻画[J].四川师范大学学报(自然科学版),2019,(06):753-757.[doi:10.3969/j.issn.1001-8395.2019.06.006]
 ZHOU Dechuan,WANG Fanggui,HU Kui.A New Characterization of PvMDS by Kronecker Function Rings[J].Journal of SichuanNormal University,2019,(06):753-757.[doi:10.3969/j.issn.1001-8395.2019.06.006]
点击复制

Kronecker函数环对PvMD的一个新刻画()
分享到:

《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2019年06期
页码:
753-757
栏目:
基础理论
出版日期:
2019-11-04

文章信息/Info

Title:
A New Characterization of PvMDS by Kronecker Function Rings
文章编号:
1001-8395(2019)06-0753-05
作者:
周德川1 王芳贵2 胡 葵1
1.西南科技大学 理学院, 四川 绵阳 621010; 2.四川师范大学 数学科学学院, 四川 成都 610066
Author(s):
ZHOU Dechuan1 WANG Fanggui2 HU Kui1
1.College of Science, Southwest University of Science and Technology, Mianyang 621010, Sichuan; 2.College of Mathematics Science, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
Kronecker函数环 w-linked overring w-平坦模 PvMD
Keywords:
Kronecker function ring w-linked overring w-flat module PvMD
分类号:
O154
DOI:
10.3969/j.issn.1001-8395.2019.06.006
文献标志码:
A
摘要:
设R是整环,若R是整闭的,则R是Prüfer整环当且仅当Kr(R,b)是平坦R[X]-模; 当且仅当Kr(R,b)是平坦R-模(Aaderson D F, Bobbs D E.J Pure Appl Algebra,1989,61:107-122.).给出这一定理在w-版本下的陈述形式,即若R是整闭整环,则R是PvMD当且仅当Kr(R,vc)是w(R[X])-平坦R[X]-模; 当且仅当Kr(R,vc)是w-平坦R-模.
Abstract:
In this paper, we show that if R is integrally closed, then R is a PvMD if and only if Kr(R, vc) is a w(R[X])-flat R[X]-module; if and only if Kr(R, vc) is a w-flat R-module.This is a generalization of(Aaderson D F, Bobbs D E.J Pure Appl Algebra,1989,61:107-122.)that if R is integrally closed, then R is a Prüfer domain if and only if Kr(R, b) is a flat R[X]-module; if and only if Kr(R, b) is a flat R-module.

参考文献/References:

[1] ANDERSON D F, BOBBS D E.On treed nagata rings[J].J Pure Appl Algebra,1989,61(2):107-122.
[2] FONTANA M, HUCKABA J A.Localizing systems and semistar operations[M]//Mathematics and Its Applications.Boston:Springer-verlag,2000:169-197.
[3] GILMER R.Multiplicative Ideal Theory[M].Kingston:Queen's University,1992.
[4] ARNOLD J T.On the ideal theory of the Kronecker function ring and the domain D(X)[J].Canad J Math,1969,21(1):558-563.
[5] GILMER R.An embedding theorem for HCF-rings[J].Proc Cambridge Philos Soc,1970,68(3):583-587.
[6] ARNOLD J T, BREWER J W.Kronecker function ring and flat D[X]-modules[J].Proc Am Math Soc,1971,27(3):483-485.
[7] CHANG G W.Prüfer*-multiplication domains, Nagana rings, and Kronecker function rings[J].J Algebra,2008,319:309-319.
[8] WANG F G, MCCASLAND R L.On strong mori domains[J].Pure Appl Algebra,1999,135(2):155-165.
[9] CHANG G W.*-Noetherian domains and the ring D[X]N*[J].J Algebra,2006,297:216-233.
[10] 王芳贵.交换环与星型算子理论[M].北京:科学出版社,2006.
[11] 王芳贵.有限表现型模与w-凝聚环[J].四川师范大学学报(自然科学版),2010,33(1):1-9.
[12] XING S Q, WANG F G.Overrings of Prüfer v-multiplication domains[J].J Algebra Appl,2017,16(5):1750147.
[13] WANG F G, KIM H.w-injective modules and w-semi-hereditary rings[J].J Korean Math Soc,2014,51(3):509-525.
[14] RICHMAN F.Generalized quotient rings[J].Pro Am Math Soc,1965,16(4):794-799.
[15] CHANG G W, FONTANA M.Uppers to zero and semistar operations in polynomial rings[J].J Algebra,2007,318(1):484-493.
[16] PICOZZA G.A note on semistar Noetherian domains[J].Houston J Math,2007,33(2):415-431.
[17] SAHANDI P.Semistar-Krull and valuative dimension of integral domains[J].Ricerche Mat,2009,58(2):219-242.

备注/Memo

备注/Memo:
收稿日期:2018-06-20 接受日期:2019-01-28 基金项目:国家自然科学基金(11671283) 第一作者简介: 周德川(1988—),女,讲师,主要从事交换代数和同调代数的研究,E-mail:dechuan11119@sina.com
更新日期/Last Update: 2019-11-04