| Summary: | The rings considered in this article are commutative with identity. Modules are assumed to be unitary. Let R be a ring and let S be a multiplicatively closed subset of R. We say that a module M over R satisfiesS- strongaccr∗if for every submodule N of M and for every sequence <rn> of elements of R, the ascending sequence of submodules (N:Mr1)⊆(N:Mr1r2)⊆(N:Mr1r2r3)⊆⋯is S-stationary. That is, there exist k∈N and s∈S such that s(N:Mr1⋯rn)⊆(N:Mr1⋯rk)for all n≥k. We say that a ring R satisfies S- strong accr∗if R regarded as a module over R satisfies S-strong accr∗. The aim of this article is to study some basic properties of rings and modules satisfying S-strong accr∗. Keywords: Strong accr∗, S-strong accr∗, Perfect ring, S-n-acc, Mathematics Subject Classification: 13A15
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