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中文摘要：
研究一种特殊的剩余格——幂等剩余格,证明满足幂等性的一般剩余格必是可换剩余格,即不存在非可换的幂等剩余格。讨论幂等剩余格的基本性质以及与各类特殊剩余格之间的关系。在一般剩余格中引入psG-滤子的概念,给出其一组等价条件,并借助psG-滤子刻画幂等剩余格的特征。
英文摘要：
This paper is concerned with a special residuated lattice — idempotent residuated lattice,and it is proved that if a general residuated lattice is idempotent then it is commutative residuated lattice,in other words,non-commutative residuated lattice does not exist.The basic properties of idempotent residuated lattices are studied and the relation of several special residuated lattices are discussed.Moreover,in general residuated lattice the concept of psG-filter is introduced and some equivalence conditions are given.Based on these results,idempotent residuated lattice is characterized by psG-filters.
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