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Let R be a commutative ring with identity. Let R[X] and R[[X]] be the polynomial ring and the power series ring respectively over R. Being the completion of R[X] (under the X-adic topology), R[[X]] does not always share the same property with R[X] . In this paper, we present some known strange behaviors of R[[X]] compared to those of R[X] .

Some strange behaviors of the power series ring R[[X]]