Extensions of -rings
It is shown that a ring is a -ring if and only if there exists a complete orthogonal set of idempotents such that all are -rings. We also investigate -rings for Morita contexts, module extensions and power series rings.
Finitely generated projective modules and Fitting ideals.
Generalizations of morphic group rings.
Idempotent Boolean matrices.
Idempotent generated algebras and Boolean pairs
Idempotents in Group Rings.
Maps on upper triangular matrices preserving zero products
Consider —the ring of all upper triangular matrices defined over some field . A map is called a zero product preserver on in both directions if for all the condition is satisfied if and only if . In the present paper such maps are investigated. The full description of bijective zero product preservers is given. Namely, on the set of the matrices that are invertible, the map may act in any bijective way, whereas for the zero divisors and zero matrix one can write as a composition...
Nilpotent blocks and their source algebras.
Note on strongly nil clean elements in rings
Let be an associative unital ring and let be a strongly nil clean element. We introduce a new idea for examining the properties of these elements. This approach allows us to generalize some results on nil clean and strongly nil clean rings. Also, using this technique many previous proofs can be significantly shortened. Some shorter proofs concerning nil clean elements in rings in general, and in matrix rings in particular, are presented, together with some generalizations of these results.
On commuting generalized inverses of matrices and in associative rings.
On -rings
On feebly nil-clean rings
A ring is feebly nil-clean if for any there exist two orthogonal idempotents and a nilpotent such that . Let be a 2-primal feebly nil-clean ring. We prove that every matrix ring over is feebly nil-clean. The result for rings of bounded index is also obtained. These provide many classes of rings over which every matrix is the sum of orthogonal idempotent and nilpotent matrices.
On infinite periodic rings.
On periodic rings.
On products of singular elements
On rings with zero divisors. Strong -groups
On semiabelian -regular rings.
On separable extensions of group rings and quaternion rings.
On the compactness of minimal spectrum
On the rings on torsion-free groups