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中文摘要：
在BR0-代数结构中,BR0-分配性a→b∨c=（a→b）∨（a→c）具有十分重要的地位。本文证明了具有BR0-分配性的剩余格同样具备十分良好的性质。首先将BR0-分配性引入到剩余格中,并给出了BR0-分配性的等价形式。其次,在完备剩余格中将BR0-分配性进行了推广,提出了BR0-第一无限分配性和BR0-第二无限分配性。最后,分别在正则完备剩余格,单位区间[0,1]中讨论了两种BR0-无限分配性的关系及性质。
英文摘要：
BR0-distributivity has an important position in the structure of BR0-algebras which says a→b∨c=（a→b）∨（a→c）.It is proved that residuated lattices with BR0-distributivity also have good properties.BR0-distributivity is introduced in residuated lattices,and its equivalent form is given.Then the BR0-distributivity is generalized in complete residuated lattices,and BR0-first infinite distributivity and BR0-second infinite distributivity are obtained.Finally,the properties and relationship between two kinds of BR0-infinite distributivity are discussed in regular complete residuated lattices and the unite interval ,respectively.
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