On weakly periodic-like rings and commutativity theorems

Authors

  • Abu-Khuzam Hazar
  • Howard E. Bell
  • Adil Yaqub

DOI:

https://doi.org/10.5556/j.tkjm.37.2006.147

Abstract

A ring $R$ is called periodic if, for every $x$ in $R$, there exist distinct positive integers $m$ and $n$ such that $x^m=x^n$. An element $x$ of $R$ is called potent if $x^k=x$ for some integer $k>1$. A ring $R$ is called weakly periodic if every $x$ in $R$ can be written in the form $x=a+b$ for some nilpotent element $a$ and some potent element $b$ in $R$. A ring $R$ is called weakly periodic-like if every element $x$ in $R$ which is not in the center $C$ of $R$ can be written in the form $x=a+b$, with $a$ nilpotent and $b$ potent. Some structure and commutativity theorems are established for weakly periodic-like rings $R$ satisfying certain torsion-freeness hypotheses along with conditions involving some elements being central.

Author Biographies

Abu-Khuzam Hazar

Department of Mathematics, American University of Beirut, Beirut, Lebanon.

Howard E. Bell

Department of Mathematics, Brock University, St. Catharines, Ontario, Canada L2S 3A1.

Adil Yaqub

Department of Mathematics, University of California, Santa Barbara, CA 93106, USA.

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Published

2006-12-31

How to Cite

Hazar, A.-K., Bell, H. E., & Yaqub, A. . (2006). On weakly periodic-like rings and commutativity theorems. Tamkang Journal of Mathematics, 37(4), 333-343. https://doi.org/10.5556/j.tkjm.37.2006.147

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Papers