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Multiplication Modules

  • Surjeet Singh (a1) and Fazal Mehdi (a2)

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All rings R considered here are commutative with identity and all the modules are unital right modules. As defined by Mehdi [6] a module M R is said to be a multiplication module if for every pair of submodules K and N of M, KN implies K=NA for some ideal A of R. This concept generalizes the well known concept of a multiplication ring.

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References

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1. Anderson, D. D., Multiplication ideals, multiplication rings and the ring R(X), Can. J. Math. 28 (1976), 760-768.
2. Gilmer, R. W. and Mott, J. L., Multiplication rings as rings in which ideals with prime radicals are primary, Trans. Amer. Math. Soc. 114, (1965), 40-52.
3. Kaplansky, I., Infinite Abelian Groups, The University of Michigan Press, 1971.
4. Johnson, R. E. and Wong, E. T., Quasi-injective modules and irreducible rings, J. London. Math. Soc. 36 (1961), 260-268.
5. Matlis, E., Injective modules over noetherian rings, Pacific. J. Math. 8 (1958), 511-528.
6. Mehdi, F., On multiplication modules, Mathematics Student, 42 (1974), 149-153.
7. Mott, J. L., Equivalent Conditions for a ring to be a multiplication ring, Can. J. Math. 16 (1964).
8. Nakayama, T., On Frobenni-sean algebras II, Ann. of Math. 42 (1941), 1-21.
9. Zariski, O. and Samuel, P., Commutative Algebra, Vol. II, D. Van. Nostrand Company, Inc., 1960.
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Multiplication Modules

  • Surjeet Singh (a1) and Fazal Mehdi (a2)

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