Abstract
In this paper we introduce strongly prime submodules and pseudovaluation modules over an integral domain, and obtain some basic results and characterizations.
Keywords
multiplication module prime submodule strongly prime submodule valuation domain pseudo valuation domain valuation fractional submodule pseudo-valuation module
References
- 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
Abstract
References
- 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
Details
| Other ID | JA42VD98FV |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | December 1, 2011 |
| Published in Issue | Year 2011 Volume: 10 Issue: 10 |