The phrase "have a hollow ring" is commonly used to describe statements or claims that lack sincerity or truthfulness. There are various synonyms that can be used to convey the same meaning, such as "smell like a rat," "ring false," "empty promise," or "hollow claim." These phrases imply that something is not quite right or trustworthy about a statement or situation. Other synonyms include "ring hollow," "seem insincere," "have a false ring," "sound empty," or "lack substance." It is important to be aware of these phrases and use them correctly to clearly convey the intended message and tone.