A new notion of semiprime submodules
arXiv:2412.08153 · doi:10.1142/S0219498826502026
Abstract
We introduce a new concept of a semiprime submodule. We show that a submodule of a finitely generated module over a commutative ring is semiprime if and only if it is radical, that is, an intersection of prime submodules. Using our notion, we also provide a new characterization of radical submodules of finitely generated modules over commutative rings.