TY - JOUR ID - 507 TI - $(m,n)$-algebraically compactness and $(m,n)$-pure injectivity JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Behboodi, Mahmood AU - Ghorbani, Atefeh AU - Shojaee, Seyed Hossein AD - Isfahan University of Technology AD - Isfahan University of Technology AD - Isfahan university of technology Y1 - 2014 PY - 2014 VL - 40 IS - 2 SP - 433 EP - 445 KW - (n KW - m)-pure exact KW - m)-pure injective KW - m)-algebraically compact KW - pure injective KW - algebraically compact DO - N2 - 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. UR - http://bims.iranjournals.ir/article_507.html L1 - http://bims.iranjournals.ir/article_507_09d25bec7f5a7b3bdf5caa983c9d38ba.pdf ER -