剩余交换律与剩余交半格及其相关性质

首先,给出了剩余交半格的概念,通过对其性质的研究,证明了剩余交半格中的所有正则元构成的集合是交半格,并举例说明了剩余交半格中的所有正则元构成的集合不是剩余交半格;其次,证明了满足剩余交换律:x?(x→y)=y?(y→x)的正则剩余交半格是Wajsberg代数;最后,由剩余交换律:x?(x→y)=y?(y→x)得出了L是满足剩余交换律的MTL代数当且仅当L是BL代数。

The Residuated Commutative Law and the Residuated Meet Semi-lattice and Its Relative Properties

Firstly, the definition of residuated meet semi-lattice is given. Through the further study of its properties, it is proved that the set of all regular elements in the residuated meet semi-lattice is meet semi-lattice, and an example is given to illustrate the set of all regular elements in the residuated meet semi-lattice is not its substructure. Secondly, it is proved that the regular residuated meet semilattice which satisfies residuated commutative law:■(x→y)=y■(g)(y→x) is Wajsberg algebra. Finally, by the residuated commutative law:■(x→y)=y■(y→x), we obtain that L is a BL algebra, if and only if L is MTL algebra satisfying residuated commutative law.