Filters of implication reducts of basic algebras

Since basic algebras were introduced as a common generalization of MV-algebras and orthomodular lattices, their implication reducts form a common generalization of BCK-algebras and orthoimplication algebras introduced by J. C. Abbott. As shown in our previous paper, congruences in these implication reducts are in a one-to-one correspondence with their kernels. Hence, to characterize congruences it is enough to describe its kernels which is done in the paper.