论文标题
具有抗酮互动的POSET的延伸与残留结构的延伸
Extensions of posets with an antitone involution to residuated structures
论文作者
论文摘要
我们证明，每个不一定有限的POSET P =（p，\ le，'）具有抗元素相关性，可以将其扩展到残留的poset e（p）=（e（p），\ le，\ odot，\ odot，\ rightarrow，1），其中x'= x \ rightArrow0在p. in in p. in All p. if lattice ant ant ant ant atate a p.我们表明，可以通过有限的链条将Poset扩展到残留的Poset，并且可以将布尔代数（b，\ vee，\ wedge，'，p，q）扩展到残留的晶格（q，\ vee，\ vee，\ wedge，wedge，wedge，\ odot，\ odot，\ odot，\ rightarrow，\ rightarrow，1）y = y y = y y = y y y y ock in x y ock in x y ock y od x x x y ock y od x x y x x ac n x. x \ rightarrow y = x'\ vee y for l in b in B中
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.
