具有反调对合的偏序集到剩余结构的扩张
Extensions of posets with an antitone involution to residuated structures
摘要：
证明了每个具有反序对合的未必有界偏序集P=（P，\le，'）都可以扩张为剩余偏序集E（P）=（E（P），\le，\odot，\rightarrow，1），其中x'= x \rightarrow 0，对所有x \in P，如果P是具有反序对合的格，则E（P）也是格.证明了偏序集可以通过有限链扩张为剩余偏序集，布尔代数（B，\vee，\wedge，'，p，q）可以通过有限链扩张为剩余格（Q，\vee，\wedge，\odot，\rightarrow，1），使得x \odot y=x \wedge y，x \rightarrow y=x' \vee y，对所有x，y \in B.
英文摘要：
We prove that every not necessarily bounded poset P=(P,\le,') with an antitone involution can be extended to a residuated poset E(P)=(E(P),\le,\odot,\rightarrow,1) where x'=x\rightarrow0 for all x\in P. If P is a lattice with an antitone involution then E(P) is a lattice, too. We show that a poset can be extended to a residuated poset by means of a finite chain and that a Boolean algebra (B,\vee,\wedge,',p,q) can be extended to a residuated lattice (Q,\vee,\wedge,\odot,\rightarrow,1) by means of a finite chain in such a way that x\odot y=x\wedge y and x\rightarrow y=x'\vee y for all x,y\in B.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
