Weakly Prime Radical of Submodules

Year 2023, Volume: 11 Issue: 2, 105 - 108, 31.10.2023

Sibel Cansu

Abstract

In this paper, some properties of weakly prime radical are stated. The characterization of weakly prime radical for finitely generated modules is given. Also, the relationship between the weakly prime radical of a submodule and the ideals of the ring $T$ is considered.

Keywords

Prime radical, prime submodule, weakly prime radical, weakly prime submodule

References

• [1] A. Azizi, Radical formula and prime submodules, Journal of Algebra Vol:307, (2007), 454-460.
• [2] A. Azizi, Radical formula and weakly prime submodules, Glasgow Mathematical Journal of Trust Vol:51, (2009), 405-412.
• [3] M. Behboodi, On weakly prime radical of modules and semi-compatible modules, Acta Math. Hungar. Vol:113, No:3, (2006), 243-254.
• [4] M. Behboodi and H. Koohy, Weakly prime modules, Vietnam Journal of Mathematics Vol:32, No:2 (2004), 185-195.
• [5] R.L. McCasland and M.E. Moore, On radical of submodules, Communications in Algebra Vol:19, No:5, (1991), 1327-1341.
• [6] E. Yılmaz and S. K. Cansu, Baer’s lower nilradical and classical prime submodules, Bulletin of the Iranian Mathematical Society Vol:40, No:5, (2014), 1263-1274.
• [7] C-P. Lu, Prime submodules of modules, Comment. Math. University Sancti Pauli Vol:33, No:1, (1984), 61-69.