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Mar 3, 2021 at 19:26 comment added Alex Kruckman This argument is almost identical to an exercise I assigned recently in my commutative algebra class: every nonzero commutative ring has a minimal prime ideal.
Mar 3, 2021 at 19:25 comment added Dominic van der Zypen Thanks for your argument, somehow I was convinced that the intersection argument wouldn't work - and thanks to you, I learned something today!
Mar 3, 2021 at 19:24 vote accept Dominic van der Zypen
Mar 3, 2021 at 19:11 history answered Alex Kruckman CC BY-SA 4.0