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2 results

  • 4 - Objects of Type Π / ⨿

  • Radoslav Dimitric
  • Book:
    Slenderness
    Published online:
    30 November 2018
    Print publication:
    06 December 2018, pp 150-188

  • Summary

    Infinite product over infinite coproduct is an object of prime importance for slenderness. So is pure injectivity and purity. This chapter also looks into filtered quotients in general in order to understand thebigger picture.Countability conditions represent a watershed case. Special cases of modules and domains are examined.

  • Cotorsion modules and relative pure-injectivity

  • Part of
  • Lixin Mao, Nanqing Ding
  • Journal:
    Journal of the Australian Mathematical Society / Volume 81 / Issue 2 / October 2006
    Published online by Cambridge University Press:
    09 April 2009, pp. 225-244
    Print publication:
    October 2006
    • Article
      • You have access
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  • Let R be a ring. A right R-module C is called a cotorsion module if Ext1R (F, C) = 0 for any flat right R-module F. In this paper, we first characterize those rings satisfying the condition that every cotorsion right (left) module is injective with respect to a certain class of right (left) ideals. Then we study relative pure-injective modules and their relations with cotorsion modules.