ADDITIVE ENDOMORPHISMS GENERATED BY RING ENDOMORPHISMS

Abstract

In this paper we initiate the investigation of rings in which all the addi
tive endomorphisms AGE rings or only the left multiplication endomorphisms LGE rings are generated by ring endomorphisms This study was motivated by the recent interest in the multiplication algebra ie the K
subalgebra of EndKA generated by the left and rightmultiplications by elements of A and the identity map ofA where K is a commutative ring with unity andA is a K
algebra the work on the Sullivan Problem ie characterize those rings in which every additive endomorphism is a ring endomorphism these rings are called AE rings and the current investigation of SD
generated algebras and LSD
generated algebras