| Abstrakt: |
This article explores the concept of the power serieswise Armendariz graph of a commutative ring, denoted as PA(R). It discusses various properties of PA(R), including diameter, clique, and girth, and examines the relationship between the ring-theoretic properties of R and the graph-theoretic properties of PA(R). The article provides examples and proofs to support its findings. It also discusses the relationship between PA(R) and the graph of the ring R[[X]], denoted as Γ(R[[X]]), and establishes several equivalences between different statements about the graph. The article concludes by discussing the implications of these equivalences and providing a list of references for further reading. [Extracted from the article] |
