State maps on semihoops

In this paper, we introduce the notion of state maps from a semihoop to another semihoop , which is a generalization of internal states (or state operators) on a semihoop . Also we give a type of special state maps from a semihoop to , which is called internal state maps (or IS-maps). Then we give s...

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Bibliographic Details
Published in:Open mathematics (Warsaw, Poland) Poland), 2018-09, Vol.16 (1), p.1061-1076
Main Authors: Fu, Yu Long, Xin, Xiao Long, Wang, Jun Tao
Format: Article
Language:English
Subjects:
03G25
06F35
08A72
Prime SM-filter
Semihoop
SM-filter
State map
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Summary:In this paper, we introduce the notion of state maps from a semihoop to another semihoop , which is a generalization of internal states (or state operators) on a semihoop . Also we give a type of special state maps from a semihoop to , which is called internal state maps (or IS-maps). Then we give some examples and basic properties of (internal) state maps on semihoops. Moreover, we discuss the relations between state maps and internal states on other algebras. Then we introduce several kinds of filters by state maps on semihoops, called SM-filters, state filters and dual state filters, respectively, and discuss the relations among them. Furthermore we introduce and study the notion of prime SM-filters on semihoops. Finally, using SM-filter, we characterize two kinds of state semihoops.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2018-0089