ON MULTIPLICATION MODULES(V)

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Cho, Yong-Hwan (Department of Mathematics Education, and Institute of Pure and Applied Mathematics, Chonbuk National University) ;
Kim, Youn-Hyung (Department of Mathematics Education, and Institute of Pure and Applied Mathematics, Chonbuk National University)

In this paper, we find some properties of multiplication modules and give an alternative proof of a Theorem of P.F. Smith.

Ali, M.M., Smith, D.J., Finite and infinite collections of multiplication modules, Beitrage zur algebra und geometrie vol 42 (2001), 557-573.
Ali, M.M., Smith, D.J., Projective, flat and multiplication modules, New Zealand J. of Math. vol 31 (2002), 115-129.
Anderson, D.D., Some remarks on multiplication ideals, Math. Japonica vol 25 (1980), 436-469.
Anderson, D.D., Some remarks on multiplication ideals II, Comm. Algebra vol 28 (2000), 2577-2583. https://doi.org/10.1080/00927870008826980
Barnard, A., Multiplication modules, J. Algebra vol 71 (1981), 174-178. https://doi.org/10.1016/0021-8693(81)90112-5
El-bast, Z.A., Smith, P.F., Multiplication modules, Comm. in Algebra vol 16 (1988), 755-779. https://doi.org/10.1080/00927878808823601
Kaplansky, I., Commutative Rings, The University of Chicago Press (1974).
Naoum, A.G., Mijbass, A.S., Weak cancellation modules, Kyungpook Math. J vol 37 (1997), 73-82.
Naum, A.G., Flat modules and multiplication modules, Periodica Math. Hungaria vol 21(4) (1990), 309-317. https://doi.org/10.1007/BF02352695
Smith, P.F., Some remarks on multiplication modules, Arch. Math. vol 50 (1988), 223-235. https://doi.org/10.1007/BF01187738

MULTIPLICATION DEDEKIND MODULES vol.35, pp.2, 2013, https://doi.org/10.5831/HMJ.2013.35.2.173
INTEGRALLY CLOSED MODULES vol.33, pp.3, 2011, https://doi.org/10.5831/HMJ.2011.33.3.425
ON SUBMODULE TRANSFORMS T(N) AND S(N) vol.34, pp.4, 2012, https://doi.org/10.5831/HMJ.2012.34.4.505