Approximaitly prime submodules and some related concepts

Abstract EN

In this research note approximately prime submodules is defined as a new generalization of prime submodules of unitary modules over a commutative ring with identity.

A proper submodule K of an R-module Y is called an approximaitly prime submodule of Y (for short app-prime submodule), if when ever ry E K, where r E R, y E Y, implies that either y EK + soc{Y) or rY QK + soc(Y).

So, an ideal / of a ring R is called app-prime ideal of R if / is an app-prime submodule of R-module R.

Several basic properties, characterizations and examples of approximajitly prime submodules were given.

Furthermore, the definition of approximaitly prime radical of submodules of modules were introduced, and some of it is properties were established.