Prime bases of weakly prime submodules and the weak radical of submodules
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We will introduce and study the notion of prime bases for weakly prime submodules and utilize them to derive some formulas on the weak radical of submodules of a module. In particular, we will show that every one dimensional integral domain weakly satisfies the radical formula and state some necessary conditions on local integral domains which are semi-compatible or satisfy the radical formula and also on Noetherian rings which weakly satisfy the radical formula.
Abstract
We will introduce and study the notion of prime bases for weakly prime submodules and utilize them to derive some formulas on the weak radical of submodules of a module. In particular, we will show that every one dimensional integral domain weakly satisfies the radical formula and state some necessary conditions on local integral domains which are semi-compatible or satisfy the radical formula and also on Noetherian rings which weakly satisfy the radical formula.
참고문헌 (12)
- A. Azizi, "On prime and weakly prime submodules", Vietnam J. Math, 36(3), pp.315~325 (2008)
- A. Azizi, "Radical formula and prime submodules", J. Algebra, 307(1), pp.454~460 (2007)
- A. Azizi, "Radical formula and weakly prime submodules", Glasg. Math. J, 51(2), pp.405~412 (2009)
- A. Azizi, "Simplified radical formula in modules", Houston J. Math, 38(2), pp.333~344 (2012)
- M. Behboodi, "On weakly prime radical of modules and semi-compatible modules", Acta Math. Hungar, 113(3), pp.243~254 (2006)
- M. Behboodi, "Weakly prime modules", Vietnam J. Math, 32(2), pp.185~195 (2004)
- K. H. Leung, "On commutative Noetherian rings which satisfy the radical formula", Glasgow Math. J, 39(3), pp.285~293 (1997)
- S. H. Man, "On commutative Noetherian rings which satisfy the generalized radical for- mula", Comm. Algebra, 27(8), pp.4075~4088 (1999)
- R. McCasland, "On radicals of submodules of finitely generated modules", Canad. Math. Bull, 29(1), pp.37~39 (1986)
- A. Nikseresht, "On arithmetical rings and the radical formula", Vietnam J. Math, 38(1), pp.55~62 (2010)
- H. Sharif, "Rings satisfying the radical formula", Acta Math. Hungar, 71(1-2), pp.103~108 (1996)
- P. F. Smith, "Primary modules over commutative rings", Glasg. Math. J, 43(1), pp.103~111 (2001)