In this paper, we introduce and investigate the transfer of the property of coherence to the bi-amalgamation module M⋈φ,ψ(JN, J'P). We provide necessary and sufficient conditions for M⋈φ,ψ(JN, J'P) to be a coherent module.
An element in a ring R is said to be semi nil-clean if it is a sum of nilpotent and periodic elements in R. An element in a ring R is said to be semiclean if it is a sum of unit and periodic elements in R. A ring R is said to be semi nil-clean (resp., semiclean) if every element in R is semi nil-clean (resp., semiclean). We discuss some basic properties of semi nil-clean ring and we also study the concepts of semi nil-clean and semiclean properties in various context of commutative rings such as amalgamations and the ring of polynomials R[x] of a ring R.
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