… The requirement that E(A ) is a Goldie-ring is more natural than the central condition if A is
… groups whose endomorphism ring is a left Goldie-ring. Because the defining conditions of a …

… ideals of the endomorphism rings of … chain condition with respect to some radical. In this
paper we give a bound of indices of nilpotency on nil subrings of the endomorphism ring of a left …

… Let Λ be the endomorphism ring of E (L). We consider E (L) sa right /l-module so that E (L)
is an RA bimodule. We identify L with a submodule of E (L) in the obvious way. …

… For a module MA over the ring A the following conditions are … ring is a regular ring all of
whose idempotents are central. We denote by H(M) the set of all locally nilpotent endomorphisms …

… of pM and the lattice of left ideals of the endomorphism ring S= End (M) on an endo–flat …
endomorphisms in J and the intersection of kernels of endomorphisms in J are denoted by …

… application to rings of endomorphisms. In each case, a one-sided chain condition is supposed
to hold on the right. For instance, stating that R is a Goldie ring, means that in the ring R …

… ) where A is a ring with 1, u is an injective ring endomorphism of A, … conditions on A and the
Ai are as in Section 1, and that p is the cycle (1 2 ... m). We will also impose an extra condition…

… endomorphism rings. Specifically, the basic problem is to describe the projective modules
whose endomorphism rings … , it is enough to show F satisfies the descending chain condition …

… to study chain conditions on B and their relationship to chain … is a Baer ring or a right or left
upper or lower Levitzki ring), and … B is a left CS ring or a ring with finite left Goldie dimension). …

… Thus when the two chain conditions are met , the endomorphism ring must be r-regular.
After studying more closely these special chain conditions , we will establish a more complete …