대한수학회지 (Journal of the Korean Mathematical Society)

  • 제53권2호
  • /
  • Pages.475-488
  • /
  • 2016
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 투고 : 2015.03.16
  • 발행 : 2016.03.01
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초록

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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참고문헌

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