  In this paper we provide more counterexamples to Happel's question and
Snashall-Solberg's conjecture which generalize many counterexamples to these
conjectures studied in the literature. In particular, we show that a family of
$\mathbb{Z}_n\times \mathbb{Z}_n$-Galois covering algebras of quantized
exterior algebra $A_q$ in two variables answer negatively to Happel's question,
and meanwhile, the one-point coextensions of $\mathbb{Z}_n$ and
$\mathbb{Z}_n\times \mathbb{Z}_m$-Galois covering algebras of $A_q$ negate the
Snashall-Solberg's conjecture.
