Regularity in Semigroups of full Contraction Mappings
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Date
2023-12-01
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Mathematical Association of Nigeria, Kwara State
Abstract
A regular Sernigroup is a sernigroup ,g in which every elerrrent is
regular', that is, for each eleme.t a, the,e exists a, elernerrt r s,ch
that o,na,: o, while a Contraction map isl ra*ya l<l n:-g l. Let
X, be the full symmetric semigroup on X,, : {1,2,. . " , n}. Let aiso
O,, : {d e T* : (Vr,y e X.)r <.A :-+ ra I ya or ra } r1a)
and CT- = {o € T, : (Yr,1t € X,) l, - A l), ra * ya } Then CT. and OCT. be its subsemigroups of contraction
and order-preserving full contractions of Xr" This
paper investigates the regularity of the subsemigroup,
CCT. and found thal OCT. is not a regular semigroup.
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