East Asian mathematical journal

  • 제38권1호
  • /
  • Pages.1-12
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  • 2022
  • /
  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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ORE EXTENSIONS OVER σ-RIGID RINGS

  • Han, Juncheol (Department of Mathematics Education, Pusan National University) ;
  • Lee, Yang (Department of Mathematics, Yanbian University, Institute for Applied Mathematics and Optics, Hanbat National University) ;
  • Sim, Hyo-Seob (Department of Applied Mathematics, Pukyong National University)
  • 투고 : 2021.07.15
  • 심사 : 2021.09.27
  • 발행 : 2022.01.31
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초록

Let R be a ring with an endomorphism σ and a σ-derivation δ. R is called (σ, δ)-Baer (resp. (σ, δ)-quasi-Baer, (σ, δ)-p.q.-Baer, (σ, δ)-p.p.) if the right annihilator of every right (σ, δ)-set (resp., (σ, δ)-ideal, principal (σ, δ)-ideal, (σ, δ)-element) of R is generated by an idempotent of R. In this paper, for a given Ore extension A = R[x; σ, δ] of R, the following properties are investigated: If R is a σ-rigid ring in which σ and δ commute, then (1) R is (σ, δ)-Baer if and only if R is (σ, δ)-quasi-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-quasi-Baer; (2) R is (σ, δ)-p.p. if and only if R is (σ, δ)-p.q.-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.p. if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.q.-Baer.

키워드

과제정보

This work was supported by 2-year Research Grant of Pusan National University.

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