# On endo-semiprime and endo-cosemiprime modules

Document Type : Research Paper

Authors

1 Department of mathematics, Lorestan university,P.O.Box 465, Khoramabad, Iran.

2 Department of mathematics, Lorestan university, P.O.Box 465, Khoramabad, Iran.

10.29252/asta.5.1.69

Abstract

In this paper, we study the notions of endo-semiprime and endo-cosemiprime modules and obtain some related results. For instance, we show that in a right self-injective ring $R$, all nonzero ideals of $R$ are endo-semiprime as right (left) $R$-modules if and only if $R$ is semiprime. Also, we prove that both being endo-semiprime and being are Morita invariant properties.

Keywords

#### References

[1] M. Behboodi and S. H. Sojaee, On chains of classical prime submodules and dimensions theory of modules, Bull. Iranian Math. Society, 36(1) (2010), 149-166.
[2] S. Ceken, M. Alkan and P. F. Smith, Second modules over noncommutative rings, Comm. Algebra, 41 (2013), 83-98.
[3] J. Dauns, Prime modules, J. Reine Angew. Math., 298 (1978), 156-181.
[4] A. Ghorbani, Co-epi-retractable modules and co-pri rings, Comm. Algebra, 38 (2010), 3589-3596.
[5] A. Haghany and M. R. Vedadi, Endoprime modules, Acta Math. Hungar., 106(1-2) (2005), 89-99.
[6] B. Sarac, On semiprime submodules, Comm. Algebra, 37(7) (2009), 2485-2495.
[7] R. Wisbauer, Foundations of module and ring theory, Gordon and Breach Science Publishers Reading (1991).
[8] S. Yassemi,The dual notion of prime submodules, Arch. Math. Brno., 37 (2001), 273-278.