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Essentially Retractable Modules | ||
| Journal of Sciences, Islamic Republic of Iran | ||
| مقاله 8، دوره 18، شماره 4، اسفند 2007، صفحه 355-360 اصل مقاله (99.26 K) | ||
| نوع مقاله: Original Paper | ||
| نویسنده | ||
| M.R. Vedadi* | ||
| Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Islamic Republic of Iran | ||
| چکیده | ||
| We call a module essentially retractable if HomR for all essential submodules N of M. For a right FBN ring R, it is shown that: (i) A non-zero module is retractable (in the sense that HomR for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii) A non-zero module is essentially retractable if and only if there exists a prime ideal such that HomR. Over semiprime right nonsingular rings, a nonsingular essentially retractable module is precisely a module with non-zero dual. Moreover, over certain rings R, including right FBN rings, it is shown that a nonsingular module M with enough uniforms is essentially retractable if and only if there exist uniform retractable R-modules and R-homomorphisms with . | ||
| کلیدواژهها | ||
| Dual module؛ Essentially retractable؛ Homo-related | ||
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