re: Are hood vents necessary over island with electric cook top?

We lived in condos and townhomes for years, had the cheap over the stove hoods with microwave on top... smoke detectors always going off. Now we have an open floor plan house that has flat electric cooktop on island with down suction vent. No smoke alarms going off but anything good cooking, you’ll be smelling for a day or two in multiple rooms. Wish I had the money to convert to gas with hood but we probably won’t be here long so f it. We tried to get seller to replace cooktop because it has multiple cracks but they said no