Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON QUASI-COMMUTATIVE RINGS

  • Jung, Da Woon (Department of Mathematics Pusan National University) ;
  • Kim, Byung-Ok (Department of Mathematics Korea Science Academy) ;
  • Kim, Hong Kee (Department of Mathematics and RINS Gyeongsang National University) ;
  • Lee, Yang (Department of Mathematics Education Pusan National University) ;
  • Nam, Sang Bok (Department of Early Child Education Kyungdong University) ;
  • Ryu, Sung Ju (Department of Mathematics Pusan National University) ;
  • Sung, Hyo Jin (Department of Mathematics Pusan National University) ;
  • Yun, Sang Jo (Department of Mathematics Pusan National University)
  • Received : 2015.03.16
  • Published : 2016.03.01
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Abstract

We study the structure of central elements in relation with polynomial rings and introduce quasi-commutative as a generalization of commutative rings. The Jacobson radical of the polynomial ring over a quasi-commutative ring is shown to coincide with the set of all nilpotent polynomials; and locally finite quasi-commutative rings are shown to be commutative. We also provide several sorts of examples by showing the relations between quasi-commutative rings and other ring properties which have roles in ring theory. We examine next various sorts of ring extensions of quasi-commutative rings.

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References

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