余格上广义状态算子的若干性质

M. Kondo, M. Kawaguchi
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引用次数: 5

摘要

在剩馀格X和g态剩馀格(X,σ)上定义了广义态算子σ,并考虑了g态剩馀格的性质。我们证明了σ-滤波器的一个表征定理,并证明了g态残馀格(X, σ)的所有σ-滤波器的Fσ (X)类是Heyting代数。进一步证明了每个g态剩格(X, σ)是g态剩格{(X/P, σ/P)}P∈Specσ(X)的子直积的同构,其中Specσ(X)是(X, σ)的所有素数σ-滤波器的集合。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Some Properties of Generalized State Operators on Residuated Lattices
We define a generalized state operator σ on a residuated lattice X and a g-state residuated lattice (X,σ), and consider properties of g-state residuated lattices. We show that a characterization theorem of σ-filters and that the class Fσ (X) of all σ-filters of a g-state residuated lattice (X, σ) is a Heyting algebra. Moreover we prove that every g-state residuated lattice (X, σ) is isomprphic to a subdirect product of g-state residuated lattices {(X/P, σ/P)}P∈Specσ(X), where Specσ(X) is the set of all prime σ-filters of (X, σ).
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