Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 51, No. 2, pp. 417425 (2010) 

Strongly prime radical of group algebrasKanchan Joshi and R. K. SharmaDepartment of Mathematics, Indian Institute of Technology Delhi, New Delhi, India, email: kanchan.joshi@gmail.com email: rksharma@maths.iitd.ac.inAbstract: The strongly prime radical of a ring $R$, $S\msc{P}(R)$, is defined as the intersection of all strongly prime ideals of $R$. For a group algebra $KG$, we show that $S\msc{P}(KG)\cap K[\De(G)]=\msc{P}(K[\De(G)])$. We prove that the concepts of semiprime and semistrongly prime coincide in case of PI algebras. Given $S$ over $R$ is a finite normalizing extension of rings, we study the relationship of the $*$prime radicals of $S$ and $R$. Finally, we give examples of group algebras $KG$ for which $S\mathscr{P}(KG)= *$$\mathscr{P}(KG)$ and $\mathscr{P}(KG) = S\mathscr{P}(KG)$. Also an example of a group $G$ is constructed for which $\msc{P}(KG)\subsetneq *$$\msc{P}(KG)\subsetneq S\msc{P}(KG)$. Keywords: strongly prime radical, $*$prime radical, prime radical, group algebras Classification (MSC2000): 16S34, 16N60, 20C07 Full text of the article (for subscribers):
Electronic version published on: 24 Jun 2010. This page was last modified: 8 Sep 2010.
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