http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
Breaz, Simion,Cimpean, Andrada Korean Mathematical Society 2018 대한수학회보 Vol.55 No.4
We study the class of rings R with the property that for $x{\in}R$ at least one of the elements x and 1 + x are tripotent. We prove that a commutative ring has this property if and only if it is a subring of a direct product $R_0{\times}R_1{\times}R_2$ such that $R_0/J(R_0){\cong}{\mathbb{z}}_2$, for every $x{\in}J(R_0)$ we have $x^2=2x$, $R_1$ is a Boolean ring, and $R_3$ is a subring of a direct product of copies of ${\mathbb{z}}_3$.
Simion Breaz,Andrada Cimpean 대한수학회 2018 대한수학회보 Vol.55 No.4
We study the class of rings $R$ with the property that for $x\in R$ at least one of the elements $x$ and $1+x$ are tripotent. We prove that a commutative ring has this property if and only if it is a subring of a direct product $R_0\times R_1\times R_2$ such that $R_0/J(R_0)\cong \Z_2$, for every $x\in J(R_0)$ we have $x^2=2x$, $R_1$ is a Boolean ring, and $R_3$ is a subring of a direct product of copies of $\Z_3$.