Feckly McCoy环和feckly Armendariz环  

Feckly McCoy and feckly Armendariz rings

作　　者：姜美美 王尧[2] 任艳丽[3] JIANG Mei-mei;WANG Yao;REN Yan-li(School of Mathematics and Information Technology,Jiangsu Second Normal University,Nanjing 210013,Jiangsu,China;School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,Jiangsu,China;School of Information Engineering,Nanjing Xiaozhuang University,Nanjing 211171,Jiangsu,China)

机构地区：[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

出　　处：《山东大学学报（理学版）》2022年第10期21-27,共7页Journal of Shandong University(Natural Science)

基　　金：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)。

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。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), rJ(pR)=aR where a∈J(R), then for each principal right ideal f(x)R[x]■J(R[x]), rJ_(R)(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.

关 键 词：feckly McCoy环 feckly Armendariz环 feckly reduced环 环扩张 

分 类 号：O153.3[理学—数学]