On Lie ideals with generalized derivations.
On non singular p-inyective rings.
A ring R is said to be left p-injective if, for any principal left ideal I of R, any left R-homomorphism I into R extends to one of R into itself. In this note left nonsingular left p-injective rings are characterized using their maximal left rings of quotients and the structure of semiprime left p-injective rings of bounded index is investigated.
On -injectivity, YJ-injectivity and quasi-Frobeniusean rings
A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characterized in terms of special annihilators. Quasi-Frobeniusean rings are characterized in terms of -injectivity....
On prime and semiprime near-rings with derivations.
On right ideals and derivations in prime rings with Engel condition
On rings close to regular and -injectivity
The following results are proved for a ring : (1) If is a fully right idempotent ring having a classical left quotient ring which is right quasi-duo, then is a strongly regular ring; (2) has a classical left quotient ring which is a finite direct sum of division rings iff is a left -ring having a reduced maximal right ideal and satisfying the maximum condition on left annihilators; (3) Let have the following properties: (a) each maximal left ideal of is either a two-sided ideal...
On rings with a unique proper essential right ideal
Right ue-rings (rings with the property of the title, i.e., with the maximality of the right socle) are investigated. It is shown that a semiprime ring R is a right ue-ring if and only if R is a regular V-ring with the socle being a maximal right ideal, and if and only if the intrinsic topology of R is non-discrete Hausdorff and dense proper right ideals are semisimple. It is proved that if R is a right self-injective right ue-ring (local right ue-ring), then R is never semiprime and is Artin semisimple...
On rings with prime centers.
On semiprime twisted semigroup rings.
On skew derivations as homomorphisms or anti-homomorphisms
Let be a prime ring with center and be a nonzero ideal of . In this manuscript, we investigate the action of skew derivation of which acts as a homomorphism or an anti-homomorphism on . Moreover, we provide an example for semiprime case.
On some additive mappings in rings with involution.
On some equations related to derivations in rings.
On strong commutativity-preserving maps.
On strongly prime semiring.
On the compactness of minimal spectrum
On the generalized hypercentralizer of a Lie ideal in a prime ring
On the Structure of Certain PP-Rings.
On von Neumann regular rings. VII.
On zero subrings and periodic subrings.
On -derivations in prime rings
Let be a 2-torsion free prime ring and let be automorphisms of . For any , set . Suppose that is a -derivation defined on . In the present paper it is shown that if satisfies , then either or is commutative if is a nonzero ideal of such that , for all , and commutes with both and , then either or is commutative. if is a nonzero ideal of such that , for all , and commutes with , then is commutative. Finally a related result has been obtain for -derivation....