On the Classical Primary Radical of Submodules
Keywords:
classical primary submodule, primary submodule, classical primary radical of submodule, primary radical of submodul, primary ideal.Abstract
In this paper we characterize the classical primary radical of submodules and classical primary submodules of modules over a commutative rings with identity. Those are extended from radical classical primary, radical primary, and primary of submodules, respectively. Moreover, we investigate relationships between classical primary radical and radical primary submodules.References
Abulebda L.J.M., The primary radical of a submodule, Advances in Pure Mathematics, Vol. 2, No. 5, pp. 344-348, 2012.
Alkan M., and Saraç B., On primary decompositions and radicals of submodules, Proceedings of the Jangjeon Mathematical Society, Vol. 10, No. 1, 71-81, 2007.
Atani S.E., and Darani A.Y., On quasi-primary submodules, Chiang Mai Journal of Science, Vol. 33, No. 3, pp. 249-254, 2006.
Atani S.E., and Saraei F.E.K., Modules which satisfy the radical formula, International Journal of Contemporary Mathematical Sciences, Vol. 2, No. 1, pp. 3-18, 2007.
Baziar M., and Behboodi M. Classical primary submodules and decomposition theory of modules, Journal of Algebra and Its Applications, vol. 8, No. 3, pp. 351-362, 2009.
Behboodi M., Jahani-Nezhad R., and Naderi M.H., Classical quasi-primary submodules, Bulletin of the Iranian Mathematical Society, Vol. 37, No. 4, pp. 51-71, 2011.
Dauns J., Prime modules, Journal für die reine und angewandte Mathematik, Vol. 298, pp. 156-181, 1978.
Fuchs L., On quasi-primary ideals, Acta Scientiarum Mathematicarum (Acta Universitatis Szegediensis), Vol. 11, pp. 174-183, 1947.
Fuchs, L., and Mosteig E., Ideal theory in Prüfer domains - an unconventional approach, Journal of Algebra, Vol. 252, No. 2, pp. 411-430, 2002.
Hedayat S., and Nekooei R., Primary decomposition of submodules of a finitely generated module over a PID, Houston Journal of Mathematics, Vol. 32, No. 2, pp. 369-377, 2006.
Jenkins J., and Smith P.F., On the prime radical of a module over a commutative ring, Communications in Algebra, Vol. 20, No. 12, pp. 593-602, 1992.
Man S.H., On commutative Noetherian rings which have the s.p.a.r. property, Archiv der Mathematik, Vol. 70, No. 1, pp. 31-40, 1998.
McCasland R.L., and Moore M.E., On radicals of submodules, Communications in Algebra, Vol. 19, No. 5, pp. 327-341, 1991.
Noether E., Idealtheorie in ring¬bereichen, Mathematische Annalen, Vol. 83, No. 1-2, pp. 24-66, 1921.
Smith P.F., Primary modules over commutative rings, Glasgow Mathematical Journal, Vol. 43, No. 1, pp. 103-111, 2001.
TiraÅŸ, Y., and Harmanci A., On prime submodules and primary decomposition, Czechoslovak Mathematical Journal, Vol. 50, No. 25, pp. 83-90, 2000.
Downloads
Additional Files
Published
Issue
Section
License
Copyright © The Author(s). This article is published under the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
