On Classical Quasi-Primary Radical of Submodules and Classical Quasi-Primary Radical Formula of Submodules
Keywords:
Classical quasi-primary submodule, classical quasi-primary radical of submodule, classical quasi-primary radical formula of submoduleAbstract
In this paper we characterize the classical quasi-primary radical of submodules and classical quasi-primary radical formula of modules over commutative rings with identity. These are extended from radical, radical primary, and radical formula of submodules, respectively. Finally, we obtain necessary and sufficient conditions of a submodule in order to be a top classical quasi-primary radical formula of submodules.
doi:10.14456/WJST.2015.37
Downloads
Metrics
References
L Fuchs. On quasi-primary ideals. Acta Univ. Szeged. Sect. Sci. Math. 1974; 11, 174-83.
L Fuchs and E Mosteig. Ideal theory in Prufer domains. J. Algebra 2002; 252, 411-30.
E Noether. Ideal theorie in Ringbereichen (in German). Math. Ann. 1992; 83, 24-66.
LJM Abulebda. The primary radical of a submodule. Adv. Pure Math. 2012; 2, 344-8.
M Alkan and B Sarac. On primary decompositions and radicals of submodules. Proc. Jangjeon Math. Soc. 2007; 10, 71-81.
S Hedayat and R Nekooei. Primary decomposition of submodules of a finitely generated module over a PID. Houston J. Math. 2006; 32, 369-77.
PF Smith. Primary modules over commutative rings. Glasgow Math. J. 2001; 43, 103-11.
Y Tlras and A Harmancl. On prime submodules and primary decomposition. Czech. Math. J. 2000; 50, 83-90.
M Baziar and M Behboodi. Classical primary submodules and decomposition theory of Modules. J. Algebra Appl. 2009; 8, 351-62.
SE Atani and AY Darani. On quasi-primary submodules. Chiang Mai J. Sci. 2006; 33, 249-54.
M Behboodi, R Jahani-Nezhad and MH Naderi. Classical quasi-primary submodules. Bull. Iran. Math. Soc. 2011; 37, 51-71.
J Dauns. Prime modules. J. Reine Angew. Math. 1978; 298, 156-81.
J Jenkins and PF Smith. On the prime radical of a module over a commutative ring. Comm. Algebra 1992; 20, 3593-602.
SH Man. On commutative noetherian rings which have the s.p.a.r. property. Arch. Math. 1998. 70, 31-40.
RL McCasland and ME Moore. On radicals of submodules. Comm. Algebra 1991; 19, 1327-41.
E Yılmaz and S Cansu. Baer’s lower nilradical and classical prime submodules. Bull. Iran. Math. Soc. 2014; 40, 1263-74.
SE Atani and FEK Saraei. Modules which satisfy the radical formula. Int. J. Contemp. Math. Sci. 2007; 2, 13-8.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Walailak Journal of Science and Technology (WJST)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.