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remark. polynomial ring [cox1997ideals, 1.1.3] [ag-0007]

Under addition and multiplication, \(R\left [x_1, \ldots , x_n\right ]\) satisfies all axioms of a commutative ring, and for this reason we will refer to \(R\left [x_1, \ldots , x_n\right ]\) as a polynomial ring.