Approximaitly quasi-primary submodules

Abstract EN

In this paper, we introduce and study the notation of approximaitly quasi-primary submodules of a unitary left R-module Q over a commutative ring R with identity.

This concept is a generalization of prime and primary submodules, where a proper submodule E of an R-module Q is called an approximaitly quasi-primary (for short App-qp) submodule of Q, if rq∈E, for r∈R, q∈Q, implies that either q∈〖rad〗_Q (E)+soc(Q) or r^n Q⊆E+soc(Q), for some n∈Z^+.

Many basic properties, examples and characterizations of this concept are introduced.