"Dogmatically" means to assert beliefs in a stubborn, rigid, or inflexible way. There are several synonyms for this word. Some of them include "authoritatively," "arrogantly," "domineeringly," and "inflexibly." Another example is "stubbornly" which means being unyielding in one's opinion. "Rigidly" suggests an unwavering adherence to rules and principles. "Obstinately" is also another synonym for "dogmatically" which suggests a persistent and stubborn refusal to comply with what is right. Regardless of the word used, it is clear that these synonyms all convey the idea of being uncompromising in one's beliefs.