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Some Notes on $$CN$$CN Rings
| Content Provider | Semantic Scholar |
|---|---|
| Author | Wei, Junchao |
| Copyright Year | 2014 |
| Abstract | A ring $$R$$R is $$CN$$CN if and only if for any $$x\in N(R)$$x∈N(R) and $$y\in R$$y∈R, $$((1+x)y)^{n+k}=(1+x)^{n+k}y^{n+k}$$((1+x)y)n+k=(1+x)n+kyn+k, where $$n$$n is a fixed positive integer and $$k=0, 1,2$$k=0,1,2; (2) Let $$R$$R be a $$CN$$CN ring and $$n\ge 1$$n≥1. If for any $$x, y\in R\backslash N(R)$$x,y∈R\N(R), $$(xy)^{n+k}=x^{n+k}y^{n+k}$$(xy)n+k=xn+kyn+k, where $$k=0, 1,2$$k=0,1,2, then $$R$$R is commutative; (3) Let $$R$$R be a ring and $$n\ge 1$$n≥1. If for any $$x\in R\backslash N(R)$$x∈R\N(R) and $$y\in R$$y∈R, $$(xy)^k=x^ky^k$$(xy)k=xkyk, $$k=n, n+1, n+2$$k=n,n+1,n+2, then $$R$$R is commutative; (4) $$NLI $$NLI exchange rings are clean. |
| Starting Page | 1589 |
| Ending Page | 1599 |
| Page Count | 11 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s40840-014-0086-9 |
| Volume Number | 38 |
| Alternate Webpage(s) | http://www.emis.de/journals/BMMSS/pdf/acceptedpapers/2012-10-051-R2.pdf |
| Alternate Webpage(s) | http://math.usm.my/bulletin/pdf/acceptedpapers/2012-10-051-R2.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s40840-014-0086-9 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Notes |
