On Strongly 2-Primal And 2-Primal Rings

Abstract

An associative ring is called 2-primal if its prime radical contains every nilpotent element of the ring ( equivalently, if every minimal prime ideal of the ring is completely prime ) and It is called a strongly 2-primal if every prime ideal of the ring is completely prime. Some results, old and new ones, connected with astrongly 2-primal rings and 2-primal rings are obtained. Also several new questions related to these rings are discussed.

R birleşmeli bir halka olsun. Eğer R nin her prime (asal) radikali halkanın tüm nilpotent elemanlarını kapsıyorsa R halkasına 2-primal halka adı verilir. Bu çalışmada 2-primal ve güçlü 2-primal (P( R /1) = N (R /1)) halkalarla ilgili bazı yeni sonuçlar elde edilmiştir.