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On page 284 Dummit and Foote in their book Abstract Algebra define a prime element in an integral domain ... as follows:

My question is as follows:

What is the definition of a prime element in a ring that is not an integral domain ... does D&F's definition imply that prime elements cannot exist in a ring that is not an integral domain ... but why not ...?

Can someone please clarify this situation ...

Peter

My question is as follows:

What is the definition of a prime element in a ring that is not an integral domain ... does D&F's definition imply that prime elements cannot exist in a ring that is not an integral domain ... but why not ...?

Can someone please clarify this situation ...

Peter