Applied-Ignition Internal Combustion Engine and Method for Operating the Internal Combustion Engine

An applied-ignition internal combustion engine includes first and second combustion chambers, an exhaust-gas system with an exhaust-gas purification system is disposed at the first and second combustion chambers, and an exhaust-gas manifold. An exhaust gas from a combustion of a fuel/air mixture firstly flows through the exhaust-gas manifold and subsequently flows through the exhaust-gas purification system. A first section of the exhaust-gas system from the first combustion chamber to the exhaust-gas purification system is cooled more than a second section of the exhaust-gas system from the second combustion chamber to the exhaust-gas purification system. The first combustion chamber is operated with a lean fuel/air mixture, the second combustion chamber is operated with a rich fuel/air mixture, and an overall exhaust-gas lambda value at an inlet into the exhaust-gas purification system is stoichiometric.