• Structure of weakly one-sided duo Ore extensions

• Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/131/0003

• Keywords

Weakly left (right) duo ring; skew polynomial ring; ore extension; rigid endomorphism; commutative ring; radical.

• Abstract

Marks (J. Algebra 280 (2004) 463–471) proved that if the skew polynomial ring $R[x; \sigma]$ is left or right duo, then $R[x; \sigma]$ is commutative. It is proved that if $R[x; \sigma]$ is weakly left (resp., right) duo over a reduced ring $R$ with an endomorphism (resp., a monomorphism) $\sigma$, then $R[x; \sigma]$ is commutative. This concludes that a noncommutative skew polynomial ring is not weakly left duo when the base ring is reduced. It is also shown that if $R[x; \sigma]$ is weakly left duo then the polynomial ring $R[x]$ is weakly left duo. We next study the structure of the Ore extension $R[x; \sigma, \delta]$ when it is weakly left or right duo.

• Author Affiliations

1. Department of Mathematics, Kyung Hee University, Seoul 02447, Korea
2. Department of Mathematics, Gyeongsang National University, Jinju 52828, Korea
3. School of Basic Sciences, Hanbat National University, Daejeon 34158, Korea
4. Department of Mathematics, Daejin University, Pocheon 11159, Korea
5. Department of Mathematics, Yanbian University, Yanji 133002, China
6. Institute of Basic Science, Daejin University, Pocheon 11159, Korea

• Proceedings – Mathematical Sciences

Volume 131, 2021
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