AI Summary & Key Takeaways
AI InsightI is strongly prime right ideal if, for each pair of a and b in R, aIb $subseteq$ I and ab $in$ I imply that either a $in$ I or b $in$ I, and we call I a strongly semiprime right ideal whenever aIa $subseteq$ I and $a^2$ $in$ I imply that a $in$ I.
📌 3 Key Takeaways
Abstract
Some characterizations of strongly regular rings will be given. Let R be a ring and $I(neq R)$ a right ideal of R. If, for each pair of right ideals A and B of R, AB $subseteq$ I implies that either A $subseteq$ I or B $subseteq$ I, then I is called a prime right ideal (or equivalently, if aRb $notsubseteq$ I whenever a and b do not belong to I). I is strongly prime right ideal if, for each pair of a and b in R, aIb $subseteq$ I and ab $in$ I imply that either a $in$ I or b $in$ I, and we call I a strongly semiprime right ideal whenever aIa $subseteq$ I and $a^2$ $in$ I imply that a $in$ I.
Özet
Kuvvetli regüler halkaların, kuvvetli asal sağ idealleri içeren bir karakterizasyonu verilmiştir.