Generalized state operators on residuated lattices
Generalized state operators on residuated lattices
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DOI：
10.1007/s00500-016-2324-6
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发表时间：
2017-10
期刊：
影响因子：
4.1
通讯作者：
M. Kondo
中科院分区：
文献类型：
--
作者：
M. Kondo
我们给出了残差格X和g态残差格上的广义态算子(g态算子)的定义，证明了所有g态残差格的类是簇的，并考虑了g态残差格的性质。我们证明了关于它们的一些基本结果，例如滤波器的表征、扩展滤波器、g态剩余晶格的同态定理。此外，我们证明每个 g 态剩余晶格都是次不可约 g 态剩余晶格的次直积。
We give a definition of a generalized state operator (g-state operator)on a residuated latticeXand a g-state residuated lattice, by which the class of all g-state residuated lattices is proved to be a variety, and consider properties of g-state residuated lattices. We prove some fundamental results about them, such as characterizations of-filters, extended-filters, homomorphism theorems for g-state residuated lattices. Moreover, we show that every g-state residuated lattice is a subdirect product of subdirectly irreducible g-state residuated lattices.