State filters in state residuated lattices

Document Type: Research Paper


1 Higher Education Complex of Bam, Iran

2 Faculty of Mathematics and computing, Higher Education Complex of Bam, Kerman, Iran.


In this paper, we introduce the notions of prime state filters, obstinate state filters, and primary state filters in state residuated lattices and study some properties of them. Several characterizations of these state filters are given and the prime state filter theorem is proved. In addition, we investigate the relations between them.


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