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In the past， people used to make clothes and do repairs on things in the house more than nowadays. I think the difference between then and now has been___1___by a number of reasons such as the quantity of other___2___， the differe

义了新的环类，即中心弱Armendariz环，通过例子说明中心弱Armendariz环是弱Armendariz环的真推广,也是中心Armendariz环的真推广.因此，对中心弱Armendariz环的研究是有意义的.作者主要给出了中心弱Armendariz环的等价刻画;说明了中心弱Armendariz环与Abelian环以及p.p.-环的关系；证明了若R是半素环且R[x]/(x2)是中心弱Armendariz，则R是约化环；若R/I是中心弱Armendar