Feckly McCoy环和feckly Armendariz环

doi:10.6040/j.issn.1671-9352.0.2021.625

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (10): 21-27.doi: 10.6040/j.issn.1671-9352.0.2021.625

• • 上一篇

Feckly McCoy环和feckly Armendariz环

姜美美¹,王尧²,任艳丽^3*

1.江苏第二师范学院数学与信息技术学院, 江苏南京 210013;2.南京信息工程大学数学与统计学院, 江苏南京 210044;3.南京晓庄学院信息工程学院, 江苏南京 211171

发布日期:2022-10-06
作者简介:姜美美(1989— ),女,博士,讲师,研究方向为环论. E-mail:meimjiang@163.com*通信作者简介:任艳丽(1965— ),女,硕士,教授,主要从事环论研究. E-mail:renyanlisx@163.com
基金资助:
国家自然科学基金资助项目(11571165);江苏省自然科学基金项目(BK20181406)

Feckly McCoy and feckly Armendariz rings

JIANG Mei-mei¹, WANG Yao², REN Yan-li^3*

1. School of Mathematics and Information Technology, Jiangsu Second Normal University, Nanjing 210013, Jiangsu, China;
2. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China;
3. School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, Jiangsu, China

Published:2022-10-06

摘要/Abstract

摘要： 讨论了feckly McCoy环和feckly Armendariz环的各类扩张性质,证明了:(1)设R是一个feckly Armendariz环,满足J(R［x］)=J(R)［x］。如果对每一个主右理想pR⊈J(R),存在a∈J(R)使得rJ_R(pR)=aR,则对每一个主右理想f(x)R［x］⊈J(R［x］),rJ_R［x］(f(x)R［x］)是由R［x］的Jacobson根中一个元素生成的理想。(2)设R是一个feckly约化环,满足J(R［x］)=J(R)［x］,则R是一个右J-APP-环当且仅当多项式环R［x］是右J-APP-环。深化了这两个新环类的研究。

关键词: feckly McCoy环, feckly Armendariz环, feckly reduced环, 环扩张

Abstract: To discuss the various extension properties of feckly McCoy rings and feckly Armendariz rings, it is proved that(1)let R be a feckly Armendariz ring with J(R［x］)=J(R)［x］, if for each principal right ideal pR⊈J(R), rJR(pR)=aR where a∈J(R), then for each principal right ideal f(x)R［x］⊈J(R［x］), rJ_R［x］(f(x)R［x］)is generated as an ideal by an element which is in the Jacobson radical of R［x］. (2)let R be a feckly reduced ring with J(R［x］)=J(R)［x］, R is a right J-APP-ring if and only if R［x］ is a right J-APP-ring. These deepen the study of these two new classes of rings.

Key words: feckly McCoy ring, feckly Armendariz ring, feckly reduced ring, extension of ring

中图分类号:

O153.3

姜美美,王尧,任艳丽. Feckly McCoy环和feckly Armendariz环[J]. 《山东大学学报(理学版)》, 2022, 57(10): 21-27.

JIANG Mei-mei, WANG Yao, REN Yan-li. Feckly McCoy and feckly Armendariz rings[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(10): 21-27.

参考文献

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Feckly McCoy环和feckly Armendariz环

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