A study on additive endomorphisms of rings
Bull. Korean Math. Soc. 2001 Vol. 38, No. 1, 149-156
Yong Uk Cho
Silla University
Abstract : In this paper, we initiate the investigation of rings in which all the additive endomorphisms are generated by ring endo\-mor\-phisms($AGE$-rings). This study was motivated by the work on the Sullivan's Research Problem [11]: Characterize those rings in which every additive endomorphism is a ring endomorphism({\it AE}-rings). The purpose of this paper is to obtain a certain characterization of $AGE$-rings, and investigate some relations between $AGE$ and $LSD$-generated rings.
Keywords : endomorphisms, $AE$-rings, $AGE$-rings, $AGOE$-rings, $LSD$-generated, $RSD$-generated and $SD$-generated
MSC numbers : 16S50
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