• Title/Summary/Keyword: rigid endomorphisms

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REFLEXIVE PROPERTY SKEWED BY RING ENDOMORPHISMS

  • Kwak, Tai Keun;Lee, Yang;Yun, Sang Jo
    • Korean Journal of Mathematics
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    • v.22 no.2
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    • pp.217-234
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    • 2014
  • Mason extended the reflexive property for subgroups to right ideals, and examined various connections between these and related concepts. A ring was usually called reflexive if the zero ideal satisfies the reflexive property. We here study this property skewed by ring endomorphisms, introducing the concept of an ${\alpha}$-skew reflexive ring, where is an endomorphism of a given ring.

NILRADICALS OF SKEW POWER SERIES RINGS

  • Hong, Chan-Yong;Kim, Nam-Kyun;Kwak, Tai-Keun
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.3
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    • pp.507-519
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    • 2004
  • For a ring endomorphism $\sigma$ of a ring R, J. Krempa called $\sigma$ a rigid endomorphism if a$\sigma$(a)=0 implies a=0 for a ${\in}$R. A ring R is called rigid if there exists a rigid endomorphism of R. In this paper, we extend the (J'-rigid property of a ring R to the upper nilradical $N_{r}$(R) of R. For an endomorphism R and the upper nilradical $N_{r}$(R) of a ring R, we introduce the condition (*): $N_{r}$(R) is a $\sigma$-ideal of R and a$\sigma$(a) ${\in}$ $N_{r}$(R) implies a ${\in}$ $N_{r}$(R) for a ${\in}$ R. We study characterizations of a ring R with an endomorphism $\sigma$ satisfying the condition (*), and we investigate their related properties. The connections between the upper nilradical of R and the upper nilradical of the skew power series ring R[[$\chi$;$\sigma$]] of R are also investigated.ated.