Not really. The sentence you've provided has a subject and a predicate; i.e. it is a full sentence. The Arabic sentence here though is a simple sentence of a noun and adjective (attributive adjective) which is attached to the noun.
The sentence you've provided would be: الأم ذكية ومشهورة - and notice how in English you've said "a mother" but in Arabic the word (Um: mother) becomes definite with AL (Al-Um), which is equivalent to "the mother" - It is better to translate by meaning and not exactly word-to-word; That's why we have a difference in definition in this word here.