“commutative algebra”的概念、定义、习题解题方法及翻译-数学辞典

单词

commutative algebra

释义

commutative algebra

The branch of algebra concerned with commutative rings, which provides the rigour and techniques for algebraic geometry. Varieties are defined as the zero sets of polynomials to which commutative rings can be associated. The geometric properties of the varieties (such as singular points) can be determined from the study of the associated rings. For example, the ring associated with the curve y2 = x2 in ℂ2 is

Note that 〈x + y〉 and 〈x−y〉 are prime ideals of ℂ[x,y] and correspond to the irreducible components x + y = 0 and x−y = 0 of the curve. See also noetherian ring.

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