The prayer of a person who does not perform ablution is invalid, and the ablution of a person who does not mention the name of Allah is invalid.
[Ibn Maajah]
Original Hadith
"«لا صلاةَ لِمن لا وُضوءَ له، ولا وُضوءَ لِمن لم يَذْكر اسم الله -تعالى- عليه».
[صحيح.] - [رواه أبو داود وابن ماجه وأحمد.]"