@article { author = {Behboodi, Mahmood and Ghorbani, Atefeh and Shojaee, Seyed Hossein}, title = {$(m,n)$-algebraically compactness and $(m,n)$-pure injectivity}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {40}, number = {2}, pages = {433-445}, year = {2014}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, abstract = {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.}, keywords = {(n,m)-pure exact,m)-pure injective,m)-algebraically compact,pure injective,algebraically compact}, url = {http://bims.iranjournals.ir/article_507.html}, eprint = {http://bims.iranjournals.ir/article_507_09d25bec7f5a7b3bdf5caa983c9d38ba.pdf} }