Regularity in Endomorphism Rings

The unique largest regular ideal Reg(A, A) in the endomorphism ring End(A) is computed for abelian groups A using the general tools developed in 7 Kasch , F. , Mader , A. ( 2005 ). Regularity and substructures of hom . Communications in Algebra 34 : 1459 – 1478 .Taylor &; Francis Online], Web of Science ®] , Google Scholar]]. This generalizes earlier results on groups with regular endomorphism ring. Interesting questions remain for a very special class of mixed abelian groups.