Open Mathematics (Sep 2018)

State maps on semihoops

  • Fu Yu Long,
  • Xin Xiao Long,
  • Wang Jun Tao

Journal volume & issue
Vol. 16, no. 1
pp. 1061 – 1076


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In this paper, we introduce the notion of state maps from a semihoop H1 to another semihoop H2, which is a generalization of internal states (or state operators) on a semihoop H. Also we give a type of special state maps from a semihoop H1 to H1, 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.