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.
On maximal chains in the lattice of module topologies.
On modules in which idempotent reducts form a chain