$(m,n)$-algebraically compactness and $(m,n)$-pure injectivity

Document Type : Research Paper


1 Isfahan University of Technology

2 Isfahan university of technology


In this paper‎, ‎we introduce the notion of $(m,n)$-‎algebr‎aically compact modules as an analogue of algebraically‎ ‎compact modules and then we show that $(m,n)$-algebraically‎ ‎compactness‎ ‎and $(m,n)$-pure injectivity for modules coincide‎. ‎Moreover‎, ‎further characterizations of a‎ ‎$(m,n)$-pure injective module over a commutative ring are given‎.


Main Subjects

  • Receive Date: 16 September 2012
  • Revise Date: 11 March 2013
  • Accept Date: 11 March 2013
  • First Publish Date: 01 April 2014