Localizations of Hereditary Noetherian Rings
*-multilinear polynomials with invertible values
New characterizations of von Neumann regular rings and a conjecture of Shamsuddin.
A theorem of Utumi states that if R is a right self-injective ring such that every maximal ideal has nonzero annihilator, then R modulo the Jacobson radical J is a finite product of simple rings and is a von Neuman regular ring. We prove two theorems and a conjecture of Shamsuddin that characterize when R itself is a von Neumann ring, using a splitting theorem of the author on when the maximal regular ideal of a ring splits off.
Normalizing extensions of semiprime rings.
Notes on generalized prime and coprime modules. I.
Notes on generalized prime and coprime modules. II.
Notes on generalized –derivation
Notes on slender prime rings
If is a prime ring such that is not completely reducible and the additive group is not complete, then is slender.
Notes on -derivations.
On a certain functional identity in prime rings. II.
On a certain identitiy satisfied by a derivation and an arbitrary additive mapping. (Summary).
On a certain identity satisfied by a derivation and an arbitrary additive mapping II.
On a certain identity satisfied by a derivation and an arbitrary additive mapping.
On a conjecture of Vukman.
On a problem of commutativity of automorphisms.
On a refinement in the classification of the nil rings
On a subset with nilpotent values in a prime ring with derivation
Let be a prime ring, with no non-zero nil right ideal, a non-zero drivation of , a non-zero two-sided ideal of . If, for any , , there exists such that , then is commutative. As a consequence we extend the result to Lie ideals.
On a theorem of J. Vukman.
On center-like elements in rings.
On centralizers of semiprime rings
Let be a semiprime ring and an additive mapping such that holds for all . Then is a left centralizer of . It is also proved that Jordan centralizers and centralizers of coincide.