The Minimal Prime Spectrum of a Commutative Ring
The Minimal Prime Spectrum of a Commutative Ring
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交换环的最小素谱
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发表时间：
1971
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通讯作者：
M. Hochster
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作者：
M. Hochster
我们称拓扑空间X为极小谱空间，如果它在通常的(壳核或Zariski)拓扑中同胚于交换环A的极小素数理想空间(见[2，第111页])。请注意，如果A有单位，则是Spec A的子空间(如[1，p.124]所定义)。众所周知，极谱空间是Hausdorff空间，并且有开基(因此是完全正则的)。给出了极谱空间的一个拓扑刻画，证明了所有极谱空间实际上都可以从有单位元的环中得到，并且极谱空间的开(而非闭)子空间是极谱的(定理1，命题5)。
We call a topological space X minspectral if it is homeomorphic to the space of minimal prime ideals of a commutative ring A in the usual (hull-kernel or Zariski) topology (see [2, p. 111]). Note that if A has an identity, is a subspace of Spec A (as defined in [1, p. 124]). It is well known that a minspectral space is Hausdorff and has a clopen basis (and hence is completely regular). We give here a topological characterization of the minspectral spaces, and we show that all minspectral spaces can actually be obtained from rings with identity and that open (but not closed) subspaces of minspectral spaces are minspectral (Theorem 1, Proposition 5).