Journal of the
Korean Mathematical Society JKMS

Some discrimination of modules whose endomorphism rings are prime is introduced, by means of structures of submodules inducing prime ideals of the endomorphism ring $\mbox{End}_R(M)$ of a left $R-$module ${}_RM$ over a ring $R$. Modules with non-prime endomorphism rings are contrapositively studied as well.

Keywords: $\cap$-prime, $+$-prime, meet-, sum-prime, openly regular, closedly regular, injective, projective modules, prime ring, Zariski topology, irreducible topology

MSC numbers: 13C99, 16D25, 16D40, 16D50