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http://dx.doi.org/10.4134/CKMS.2015.30.4.349

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)
Publication Information
Communications of the Korean Mathematical Society / v.30, no.4, 2015 , pp. 349-361 More about this Journal
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).
Keywords
order-preserving; fence; self-mapping; semigroup; coregular;
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Times Cited By KSCI : 1  (Citation Analysis)
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