On Galois projective group rings.
On Galois skew polynomial rings with inner Galois groups
On generalization of injectivity
Characterizations of quasi-continuous modules and continuous modules are given. A non-trivial generalization of injectivity (distinct from -injectivity) is considered.
On generalized formal power series
On generalized Jordan derivations of Lie triple systems
Under some conditions we prove that every generalized Jordan triple derivation on a Lie triple system is a generalized derivation. Specially, we conclude that every Jordan triple -derivation on a Lie triple system is a -derivation.
On generalized quaternion algebras.
On generalized -derivations.
On graded algebra bundles.
On -separable and Galois extensions of rings.
On induced modules over strongly group-graded algebras.
On injective -modules.
On involution rings with unique minimal *-subring.
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 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 local derivations in the Kadison sense
Let k be a field. We prove that any polynomial ring over k is a Kadison algebra if and only if k is infinite. Moreover, we present some new examples of Kadison algebras and examples of algebras which are not Kadison algebras.
On locally nilpotent endomorphisms of Gorenstein injective modules.