ON MODULES WHICH SATISFY THE RADICAL FORMULA

In this paper, we will prove representable module over a commutative ring with idendity satisfies the radical formula. A submodule N of an R-module M is said to satisfy the radical formula in M, if REM(N)=radM(N). An R-module M is said to satisfy the radical formula, if every submodule of M satisfies the radical formula in M. Moreover, it is shown that every injective modula over a commutative ring with identity whose zero ideal has a primary decomposition satisfies the radical formula. In this work, we generalize the fact that every Artinian module satisfies the radical formula.

کلیدواژه ها:

prime submodule ، radical formula ، secondary representation