FREE BOUNDED COMMUTATIVE BCK-ALGEBRA WITH ONE FREE GENERATOR
Tadeusz Traczyk · Demonstratio Mathematica · 1983
Let (A; 0, 1) be a bounded commutative BCK-algebra.As is now well known, A is a distributive lattice with respect to the derived BCK-order x«y if and only if xy = 0.It is shown that every 1-generated bounded commutative BCK-chain is either finite or isomorphic tò certain ordinal sum of chains of integers A = iti), where I is finite and the SCK-product in A is defined by the subtraction of numbers.Moreover the free 1-generated bounded commutative BCK-algebra is isomorphic to a certain subdirect product of those sums.