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3 results

  • ACCESSIBLE SUBRINGS AND KUROSH’S CHAINS OF ASSOCIATIVE RINGS

  • Part of
  • RYSZARD R. ANDRUSZKIEWICZ, MAGDALENA SOBOLEWSKA
  • Journal:
    Journal of the Australian Mathematical Society / Volume 95 / Issue 2 / October 2013
    Published online by Cambridge University Press:
    18 July 2013, pp. 145-157
    Print publication:
    October 2013
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  • This article is devoted to the historical study of the ADS-problem with a special emphasis on the use of methods and techniques, emerging with the development of the theory of rings: accessible subrings, iterated maximal essential extensions of rings, completely normal rings. We construct new examples of classes for which Kurosh’s chain stabilizes at any given step. We recall the old nontrivial questions, and we pose a new one.

  • ON CONTINUOUS AND ADJOINT MORPHISMS BETWEEN NON-COMMUTATIVE PRIME SPECTRA

  • Edward S. Letzter
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 49 / Issue 2 / June 2006
    Published online by Cambridge University Press:
    30 May 2006, pp. 367-381
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  • We study topological properties of the correspondence of prime spectra associated with a non-commutative ring homomorphism $R\rightarrow S$. Our main result provides criteria for the adjointness of certain functors between the categories of Zariski closed subsets of $\spec R$ and $\spec S$; these functors arise naturally from restriction and extension of scalars. When $R$ and $S$ are left Noetherian, adjointness occurs only for centralizing and ‘nearly centralizing’ homomorphisms.