Modules whose countably generated submodules are epimorphic images
Modules with semiregular endomorphism rings
We characterize the semiregularity of the endomorphism ring of a module with respect to the ideal of endomorphisms with large kernel, and show some new classes of modules with semiregular endomorphism rings.
More on matrix near-rings.
Most abelian p-groups are determined by the Jacobson radical of their endomorphism rings.
Necklace rings and their radicals.
Nil-clean and unit-regular elements in certain subrings of
An element in a ring is clean (or, unit-regular) if it is the sum (or, the product) of an idempotent and a unit, and is nil-clean if it is the sum of an idempotent and a nilpotent. Firstly, we show that Jacobson’s lemma does not hold for nil-clean elements in a ring, answering a question posed by Koşan, Wang and Zhou (2016). Secondly, we present new counter-examples to Diesl’s question whether a nil-clean element is clean in a ring. Lastly, we give new examples of unit-regular elements that are...
Non-linear maps preserving ideals on a parabolic subalgebra of a simple algebra
Let be an arbitrary parabolic subalgebra of a simple associative -algebra. The ideals of are determined completely; Each ideal of is shown to be generated by one element; Every non-linear invertible map on that preserves ideals is described in an explicit formula.
Nonlinear maps preserving Lie products on triangular algebras
In this paper we prove that every bijection preserving Lie products from a triangular algebra onto a normal triangular algebra is additive modulo centre. As an application, we described the form of bijections preserving Lie products on nest algebras and block upper triangular matrix algebras.
Normal radicals of endomorphism rings of free and projective modules
Normal structure of the adjoint group in the radical rings .
Odd H-depth and H-separable extensions
Let C n(A,B) be the relative Hochschild bar resolution groups of a subring B ⊆ A. The subring pair has right depth 2n if C n+1(A,B) is isomorphic to a direct summand of a multiple of C n(A,B) as A-B-bimodules; depth 2n + 1 if the same condition holds only as B-B-bimodules. It is then natural to ask what is defined if this same condition should hold as A-A-bimodules, the so-called H-depth 2n − 1 condition. In particular, the H-depth 1 condition coincides with A being an H-separable extension of B....
On derivations over rings of triangular matrices
On endomorphism algebras over admissible Dedekind domains
On Endomorphism Rings of Primary Abelian Groups.
On Endomorphism Rings of Quasiprojective Modules.
On endomorphisms and quasi-endomorphisms of torsionfree groups
On graphs associated to rings.
On Groups and Endomorphism Rings.
On lifting of idempotents and semiregular endomorphism rings
Starting with some observations on (strong) lifting of idempotents, we characterize a module whose endomorphism ring is semiregular with respect to the ideal of endomorphisms with small image. This is the dual of Yamagata's work [Colloq. Math. 113 (2008)] on a module whose endomorphism ring is semiregular with respect to the ideal of endomorphisms with large kernel.
On matrix near-rings.