Canadian mathematical bulletin | |
Rings in Which Every Element is a Sum of Two Tripotents | |
Tamer Ko?an3  Zhiling Ying1  Yiqiang Zhou2  | |
[1] College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, P.R. China;Department of Mathematics and Statistics, Memorial University of Newfoundland, St.John's, NL A1C 5S7, Canada;Department of Mathematics, Gebze Technical University, Gebze/Kocaeli, Turkey | |
关键词: idempotent; tripotent; Boolean ring; polynomial identity $x^3=x$; polynomial identity $x^6=x^4$; polynomial identity $x^8=x^4$; | |
DOI : 10.4153/CMB-2016-009-0 | |
学科分类:数学(综合) | |
来源: University of Toronto Press * Journals Division | |
【 摘 要 】
Let $R$ be a ring. The following results are proved: $(1)$ every element of $R$ is a sum of an idempotent and a tripotent that commute iff $R$ has the identity $x^6=x^4$ iff $Rcong R_1imes R_2$, where $R_1/J(R_1)$ is Boolean with $U(R_1)$ a group of exponent $2$ and $R_2$ is zero or a subdirect product of $mathbb Z_3$'s; $(2)$ every element of $R$ is either a sum or a difference of two commuting idempotents iff $Rcong R_1imes R_2$, where $R_1/J(R_1)$ is Boolean with $J(R_1)=0$ or $J(R_1)={0,2}$, and $R_2$ is zero or a subdirect product of $mathbb Z_3$'s; $(3)$ every element of $R$ is a sum of two commuting tripotents iff $Rcong R_1imes R_2imes R_3$, where $R_1/J(R_1)$ is Boolean with $U(R_1)$ a group of exponent $2$, $R_2$ is zero or a subdirect product of $mathbb Z_3$'s, and $R_3$ is zero or a subdirectproduct of $mathbb Z_5$'s.
【 授权许可】
Unknown
【 预 览 】
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RO201912050577240ZK.pdf | 25KB | download |