Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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QUASI-COMMUTATIVITY RELATED TO POWERS

  • Kim, Hyun-Min (Department of Mathematics Pusan National University) ;
  • Li, Dan (Department of Mathematics Pusan National University) ;
  • Piao, Zhelin (Department of Mathematics Yanbian University)
  • Received : 2016.09.26
  • Accepted : 2017.03.15
  • Published : 2017.11.30
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Abstract

We study the quasi-commutativity in relation with powers of coefficients of polynomials. In the procedure we introduce the concept of ${\pi}$-quasi-commutative ring as a generalization of quasi-commutative rings. We show first that every ${\pi}$-quasi-commutative ring is Abelian and that a locally finite Abelian ring is ${\pi}$-quasi-commutative. The role of these facts are essential to our study in this note. The structures of various sorts of ${\pi}$-quasi-commutative rings are investigated to answer the questions raised naturally in the process, in relation to the structure of Jacobson and nil radicals.

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References

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