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Q-modules | ||
| Tikrit Journal of Pure Science | ||
| Article 1, Volume 15, Issue 1, 2010, Pages 266-273 | ||
| Authors | ||
| Ali S. Mijbass; Hibat K. Mohammadali | ||
| Abstract | ||
| Let R be a commutative ring with identity and all R-modules are unitary. A ring R is called q-ring if every ideal of R is quasi-injective . In this work, we introduce the concept of Q-module as a generalization for the concept of q-ring. An R-module M is said to be a Q-module if every R-submodule of M is quasi-injective. We characterize such modules and study their properties . Relationships between Q-modules and other classes of modules are given. Q-modules are studied over artinian ring. Endomorphisms rings of Q-modules are examined. MSC(2000): 13C11,13C13,13C99,16P20. Key words: Q-module, quasi-injective module, fully invariant subomdule,duo module, quasi-invertible submodule, quasi-Dedekind module, cohopfian module, hopfian module, artinian ring, Endomorphisms ring , uniform module. | ||
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