Consider $k[X,Y]/(X+Y)$ where k is a field. The task is to find the prime ideals of that ring. As far as I know, these correspond to the prime Ideals of $k[X,Y]$ that contain $(X+Y)$. Since this is generated by one element, namely $(X+Y)$, these must devide $(X+Y)$. The only prime ideal that does so would be $(X+Y)$. Therefore the only prime Ideal of $k[X,Y]/(X+Y)$ is $(X+Y)$. Is this correct or are there mistakes in my argumentation? Also, do I need to care for the (0) Ideal at one point? Thanks in advance!
2026-03-29 23:58:23.1774828703
Prime ideals in Quotientring
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