Here’s an interesting question…(adsbygoogle = window.adsbygoogle || []).push({});

Let R be a commutative ring and ‘a’ an element in R. If the principal ideal Ra is a maximal ideal of R then show that ‘a’ is an irreducible element.

If a is prime, this is pretty obvious…if a is not prime, then we say a= bc for some b,c in R. Now we need to show that either of them is a unit. I can’t imagine how…

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# Irreducible elements

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