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Reflexive property skewed by ring endomorphisms

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Mason extended the reflexive property for subgroups to right ideals, and examined various connections between these and related concepts. A ring was usually called it reflexive if the zero ideal satisfies the reflexive property. We here study this property skewed by ring endomorphisms, introducing the concept of an it alpha-skew reflexive ring, where alpha is an endomorphism of a given ring.

Abstract

Mason extended the reflexive property for subgroups to right ideals, and examined various connections between these and related concepts. A ring was usually called it reflexive if the zero ideal satisfies the reflexive property. We here study this property skewed by ring endomorphisms, introducing the concept of an it alpha-skew reflexive ring, where alpha is an endomorphism of a given ring.

참고문헌 (12)

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  2. M. Baser, "On Extended Reversible Rings", Algebra Colloq, 16, pp.37~48 (2009)
  3. H.E. Bell, "Near-rings in which each element is a power of itself", Bull. Austral. Math. Soc, 2, pp.363~368 (1970)
  4. P. M. Cohn, "Reversible rings", Bull. London Math. Soc, 32, pp.641~648 (1999)
  5. J.L. Dorroh, "Concerning adjunctins to algebras", Bull. Amer. Math. Soc, 38, pp.85~88 (1932)
  6. Y. Hirano, "On annihilator ideals of a polynomial ring over a noncommutative ring", J. Pure Appl. Algebra, 168, pp.45~52 (2002)
  7. C. Y. Hong, "Ore extensions of Baer and p.p.-rings", J. Pure Appl. Algebra, 151, pp.215~226 (2000)
  8. N.K. Kim, "Armendariz rings and reduced rings", J. Algebra, 223, pp.477~488 (2000)
  9. J. Krempa, "Some examples of reduced rings", Algebra Colloq, 3, pp.289~300 (1996)
  10. T.K. Kwak, "Reflexive property of rings", Comm. Algebra, 40, pp.1576~1594 (2012)
  11. G. Mason, "Reflexive ideals", Comm. Algebra, 9, pp.1709~1724 (1981)
  12. J.C. McConnell, "Noncommutative Noetherian Rings" (1987), John Wiley & Sons Ltd.

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