Taiwanese Journal of Mathematics


Shahabaddin Ebrahimi Atani

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Let R be a commutative ring with identity (zero-divisors admitted). Various properties of submodules a multiplication module are considered. In fact, our aim here is to generalize some of the results in the paper listed as [1], from finitely generated faithful multiplication ideals to finitely generated faithful multiplication modules.

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Taiwanese J. Math., Volume 9, Number 3 (2005), 385-396.

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

Primary: 13A15: Ideals; multiplicative ideal theory 13F05: Dedekind, Prüfer, Krull and Mori rings and their generalizations

multiplication modules greatest common divisor least common multiple


Atani, Shahabaddin Ebrahimi. SUBMODULES OF MULTIPLICATION MODULES. Taiwanese J. Math. 9 (2005), no. 3, 385--396. doi:10.11650/twjm/1500407847. https://projecteuclid.org/euclid.twjm/1500407847

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  • [1.] M. M. Ali, and D. J. Smith, Generalized GCD rings, Beitr$\ddot{a}$ge Algebra Geom., 42 (2001), 219-233.
  • [2.] R. Ameri, On the prime submodules of multiplication modules, Inter. J. of Mathematics and Mathematical Sciences, 27 (2003), 1715-1724.
  • [3.] D. D. Anderson, Some remarks on multiplication ideals, Math. Japonica, 25 (1980), 463-469.
  • [4.] D. D. Anderson, D. D. Some remarks on multiplication ideals, II, Comm. Algebra, 28 (2000), 2577-2583.
  • [5.] D. D. Anderson and D. F. Anderson, Generalized GCD domains, Comment. Math. Univ. St. Paul, 2 (1979), 215-221.
  • [6.] D. D. Anderson, $\pi$-domains, divisioral ideals and overrings, Glasgow Math. J, 19 (1978), 199-203.
  • [7.] Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16 (1988), 755-779.
  • [8.] S. Ebrahimi Atani, On secondary modules over pullback rings, Comm. Algebra, 30 (2002), 2675-2685.
  • [9.] S. Ebrahimi Atani, Submodules of secondary modules, Inter. J. of Mathematics and Mathematical Sciences, 31 (2002), 321-327.
  • [10.] J. A. Huckaba, Commutative Rings with Zero Divisors, Marcel Dekker, Inc, New York, 1988.
  • [11.] G. H. Low and P. F. Smith, Multiplication modules and ideals, Comm. Algebra, 18 (1990), 4353-4375.
  • [12.] A. G. Naoum and A. S. Mijbass, Weak cancellation modules, Kyungpook Math. J., 37 (1997), 73-82.
  • [13.] P. F. Smith, Some remarks on multiplication modules, Arch. Math, \bf50 (1988), 223-235.