On \phi prime submodules
Keywords:
Prime submodule; φ-prime submodule
Abstract
In this paper, we study some properties of φ-prime submodules and
we give another charactrization for it. For given submodules N and K of a module
M with K ⊆ N, we prove that N is φ-prime submodule if and only if N/K
is φ_K-prime submodule. Finally, we show that any finite sum of φ-prime submodules is
φ-prime.
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References
[1] J. Jenkins and P. F. Smith, On the prime radical of a module over a commutative ring, Comm. Algebra 20(1992), 3593-3602.
[2] C. P. Lu, Prime submodules, Comm. Math. Univ. Sancti Pauli 33 (1984),
61-69.
[3] C. P. Lu, Prime submodule of modules, Comm. Math. Univ. Sancti Pauli 33
(1984), 6169.
[4] R. L. McCasland and M. E. Moore, Prime submodules, Comm. Algebra, 20(6)
(1992), 1803-1817.
[5] R. Sharp, Steps in commutative algebra, Cambridge University Press,
Cambridge-New York-Sydney, 2000.
[6] N. Zamani, Φ-prime submodules, Glasgow mathematical journal, 52(02)
(2010), 253 - 259.
[2] C. P. Lu, Prime submodules, Comm. Math. Univ. Sancti Pauli 33 (1984),
61-69.
[3] C. P. Lu, Prime submodule of modules, Comm. Math. Univ. Sancti Pauli 33
(1984), 6169.
[4] R. L. McCasland and M. E. Moore, Prime submodules, Comm. Algebra, 20(6)
(1992), 1803-1817.
[5] R. Sharp, Steps in commutative algebra, Cambridge University Press,
Cambridge-New York-Sydney, 2000.
[6] N. Zamani, Φ-prime submodules, Glasgow mathematical journal, 52(02)
(2010), 253 - 259.
Published
2021-08-10
How to Cite
akray, ismael. (2021). On \phi prime submodules. Al-Qadisiyah Journal of Pure Science, 26(4), 288–292. https://doi.org/10.29350/qjps.2021.26.4.1374
Section
Special Issue (Silver Jubilee)
Copyright © Author(s) . This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
