Complete retract mappings of a complete lattice ordered group
Ján Jakubík · Czechoslovak Mathematical Journal · 1993
Retracts of partially ordered sets were studied in [2]-[5].Retracts of abelian lattice ordered groups were dealt with in [6].In [7], retract varieties of abelian lattice ordered groups were investigated.An endomorphism / of a lattice ordered group H is said to be a complete retract (cf.[6]) if it satisfies the following conditions: (i) /(/(A)) = A for each A G H; (ii) if {A.}, 6/ C //, A G H, A = V A, holds in H, then /(A) = V /(A,), and dually.The following results concern the relations between complete retract mappings and direct decompositions of a lattice ordered group H. (A) Let H be an internal direct product of its l-subgroups A\, A2 an d A3. For h € H let hi (i G {1,2,3}) be the component of h in A{. Assume that