STRONGLY PRIME SUBMODULES AND PSEUDO-VALUATION MODULES

In this paper we introduce strongly prime submodules and pseudovaluation modules over an integral domain, and obtain some basic results and characterizations.

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  • Z. Abd El-bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16(4) (1988), 755–779.
  • M. Alkan, B. Sarac and Y. Tiras, Dedekind modules, Comm. Algebra, 33(5) (2005), 1617–1626.
  • M. Alkan and Y. Tiras, On invertible and dense submodules, Comm. Algebra, (10) (2004), 3911–3919.
  • R. Ameri, On the prime submodules of multiplication modules, Int. J. Math. Math. Sci., 27 (2003), 1715–1724.
  • M. F. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley, 1969.
  • N. Bourbaki, Commutative Algebra, Addison-Wesley, 1972.
  • J. R. Hedstrom and Evan G. Houston, Pseudo-valuation domains, Pacific J. Math., 75(1) (1978), 137–147.
  • J. R. Hedstrom and E. G. Houston, Pseudo-valuation domains (II), Houston J. Math., 4(2) (1978), 199–207.
  • J. A. Huckaba, Extensions of pseudo-valuations, Pacific J. Math. 29(2) (1969), –302.
  • M. D. Larsen and P. J. McCarthy, Multiplicative Theory of Ideals, Academic Press, London, 1971.
  • J. Moghaderi and R. Nekooei, Valuation, discrete valuation and Dedekind mod- ules, Int. Electron. J. Algebra, 8 (2010), 18–29.
  • A. G. Naoum and F. H. Al-Alwan, Dedekind modules, Comm. Algebra, 24(2) (1996), 397–412.
  • R. Nekooei, On finitely generated multiplication modules, Czechoslovak Math. J., 55(130)(2005), 503–510.
  • P. F. Smith, Some remarks on multiplication modules, Arch. Math., 50(1988), –235. J. Moghaderi
  • Department of Mathematics Hormozgan University Bandar Abbas, Iran e-mail: j.moghaderi@yahoo.com R. Nekooei Department of Mathematics Shahid Bahonar University of Kerman Kerman, Iran e-mail: rnekooei@mail.uk.ac.ir