On commutativity of one-sided -unital rings.
On dependent elements in rings.
On derivations and commutativity in prime rings.
On equivalence of graded rings.
On finiteness conditions for subalgebras with zero multiplication
Let F be a commutative ring with unit. In this paper, for an associative F-algebra A we study some properties forced by finite length or DCC condition on F-submodules of A that are subalgebras with zero multiplication. Such conditions were considered earlier when F was either a field or the ring of rational integers. In the final section, we consider algebras with maximal commutative subalgebras of finite length as F-modules and obtain some results parallel to those known for ACC condition or finite...
On Jordan ideals and derivations in rings with involution
Let be a -torsion free -prime ring, a derivation which commutes with and a -Jordan ideal and a subring of . In this paper, it is shown that if either acts as a homomorphism or as an anti-homomorphism on , then or . Furthermore, an example is given to demonstrate that the -primeness hypothesis is not superfluous.
On Jordan ideals and left -derivations in prime rings.
On left -derivations of prime rings
Let be a -torsion free prime ring. Suppose that are automorphisms of . In the present paper it is established that if admits a nonzero Jordan left -derivation, then is commutative. Further, as an application of this resul it is shown that every Jordan left -derivation on is a left -derivation on . Finally, in case of an arbitrary prime ring it is proved that if admits a left -derivation which acts also as a homomorphism (resp. anti-homomorphism) on a nonzero ideal of , then ...
On Lie ideals and Jordan left derivations of prime rings
Let be a 2-torsion free prime ring and let be a Lie ideal of such that for all . In the present paper it is shown that if is an additive mappings of into itself satisfying for all , then for all .
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.