%0 Journal Article %T $(m,n)$-algebraically compactness and $(m,n)$-pure injectivity %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Behboodi, Mahmood %A Ghorbani, Atefeh %A Shojaee, Seyed Hossein %D 2014 %\ 04/01/2014 %V 40 %N 2 %P 433-445 %! $(m,n)$-algebraically compactness and $(m,n)$-pure injectivity %K (n %K m)-pure exact %K m)-pure injective %K m)-algebraically compact %K pure injective %K algebraically compact %R %X 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. %U http://bims.iranjournals.ir/article_507_09d25bec7f5a7b3bdf5caa983c9d38ba.pdf