# COREGULARITY OF ORDER-PRESERVING SELF-MAPPING SEMIGROUPS OF FENCES

• JENDANA, KETSARIN (Department of Mathematics Faculty of Science Silpakorn University) ;
• SRITHUS, RATANA (Department of Mathematics Faculty of Science Silpakorn University)
• Received : 2015.03.10
• Published : 2015.10.31

#### Abstract

A fence is an ordered set that the order forms a path with alternating orientation. Let F = (F;${\leq}$) be a fence and let OT(F) be the semigroup of all order-preserving self-mappings of F. We prove that OT(F) is coregular if and only if ${\mid}F{\mid}{\leq}2$. We characterize all coregular elements in OT(F) when F is finite. For any subfence S of F, we show that the set COTS(F) of all order-preserving self-mappings in OT(F) having S as their range forms a coregular subsemigroup of OT(F). Under some conditions, we show that a union of COTS(F)'s forms a coregular subsemigroup of OT(F).

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