This question was made during a class of Computer Theory in Rome, Italy.
Let $G$ be a regular grammar, $\Sigma$ its alphabet and $L(G)$ the language generated by $G$
Given a regular grammar $G$, is $L(G) = \Sigma^*$ a decidable property?
I can design a Finite State Automaton that recognize the strings in the language $G$. Because regular languages are closed under the iteration operation, the FSA recognize also string in $\Sigma^*$ alphabet