再论约化环的零因子图和零化理想图
A little more on the zero-divisor graph and the annihilating-ideal graph of a reduced ring
摘要：
我们试图将AG（R）和Gamma（R）的一些图的性质转化为Zebraki拓扑的拓扑性质。证明了Rad（Gamma（R））与Rad（AG（R））相等且等于3，当且仅当R的零理想是反不动位理想，当且仅当Min（R）不存在孤立点，当且仅当Gamma（R）是三角剖分的，当且仅当AG（R）是三角剖分的.同时，我们证明了如果环R的零理想是固定位理想，则dtt（AG（R））=| B（R）|而且如果另外|最小值（R）|> 2，则dt（AG（R））=| B（R）|.最后，证明了dt（AG（R））是有限的，当且仅当dtt（AG（R））是有限的;当且仅当Min（R）是有限的。
英文摘要：
We have tried to translate some graph properties of AG(R) and Gamma(R) to the topological properties of Zariski topology. We prove that Rad(Gamma(R)) and Rad(AG(R)) are equal and they are equal to 3, if and only if the zero ideal of R is an anti fixed-place ideal, if and only if Min(R) does not have any isolated point, if and only if Gamma(R) is triangulated, if and only if AG(R) is triangulated. Also, we show that if the zero ideal of a ring R is a fixed-place ideal, then dtt(AG(R)) = |B(R)| and also if in addition |Min(R)| > 2, then dt(AG(R)) = |B(R)|. Finally, it has been shown that dt(AG(R)) is finite, if and only if dtt(AG(R) is finite; if and only if Min(R) is finite.
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