关于Weakly J-Clean环OACSTPCD
On Weakly J-Clean Rings
一个环 R叫做w eakly J‐clean环，如果R中的每一个元素都可以写成a＝ e＋ j或a＝－e＋ j的形式，其中e是幂等元，j属于Jacobson根。文章探究了weakly J‐clean环的各种性质，证明了 R是weakly J‐clean环当且仅当 R是clean环并且 R／J（R）是弱布尔环，当且仅当R／6 R是w eakly J‐clean环且幂等元关于 J（R）可以提升。一个环R是唯一w eakly nil clean环当且仅当…查看全部>>
A ring R is called a weakly J‐clean ring if every element a∈ R can be written in the form of a=e+ j or a= -e+ j where e is an idempotent and j belongs to the Jacobson radical .The paper explores various properties of weakly J‐clean rings ,proves that a ring R is weakly J‐clean if and only if R is clean and R/J(R) is weakly Boolean ,if and only if R/6R is weakly J‐clean and idempotents can lift J(R) .A ring R is uniquely weakly nil clean if and only if R is a…查看全部>>
沈洪地;陈焕艮
杭州师范大学理学院，浙江 杭州 310036杭州师范大学理学院，浙江 杭州 310036
数理科学
weakly J-clean环clean环唯一weakly nil clean环幂等元Jacobson根
weakly J-clean ringclean ringuniquely weakly nil clean ringidempotentJacobson radical
《杭州师范大学学报（自然科学版）》 2015 (6)
616-624,9
Supported by the Natural Science Foundation of Zhejiang Province （LY13A010019）．
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