Counterexamples to Wang's Conjectures 3.26 and 5.3 on semigroup algebras

We refute Conjectures 3.26 and 5.3 of Wang's Semigroup rings and algebraically independent sequences with respect to idempotents in commutative semigroups (arXiv:2509.18724v1, pp. 23 and 27). The commutative periodic monoid of finite subsets of the natural numbers, paired with levels zero, one and two under union and capped addition, has algebraic Davenport constant one over every nonzero commutative unitary ring. Its nongroup relative Davenport constants are unbounded. The finite submonoids with supports contained in {1,...,m}, m>=1, have the same algebraic constant, whereas the expression conjectured to equal it grows without bound as m increases.