implications, coimplications and left semi-uninorms on a complete lattice

in this paper, we firstly show that the $n$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $n$-dual operation. as a dual result, the $n$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $wedge$-distributive left semi-uninorm, is the right residual implication induced by its $n$-dual operation. then, we demonstrate that the $n$-dual operations of the left semi-uninorms induced by an implication and a coimplication, which satisfy the neutrality principle, are the left semi-uninorms. finally, we reveal the relationships between conjunctive right arbitrary $vee$-distributive left semi-uninorms induced by implications and disjunctive right arbitrary $wedge$-distributive left semi-uninorms induced by coimplications, where both implications and coimplications satisfy the neutrality principle.