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On G -disconnected injective models

Marek Golasiński (2003)

Annales de l’institut Fourier

Let G be a finite group. It was observed by L.S. Scull that the original definition of the equivariant minimality in the G -connected case is incorrect because of an error concerning algebraic properties. In the G -disconnected case the orbit category 𝒪 ( G ) was originally replaced by the category 𝒪 ( G , X ) with one object for each component of each fixed point simplicial subsets X H of a G -simplicial set X , for all subgroups H ⊆ G . We redefine the equivariant minimality and redevelop some results on the rational homotopy...

On generalization of injectivity

Roger Yue Chi Ming (1992)

Archivum Mathematicum

Characterizations of quasi-continuous modules and continuous modules are given. A non-trivial generalization of injectivity (distinct from p -injectivity) is considered.

On generalized Jordan derivations of Lie triple systems

Abbas Najati (2010)

Czechoslovak Mathematical Journal

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 θ -derivation on a Lie triple system is a θ -derivation.

On Jordan ideals and derivations in rings with involution

Lahcen Oukhtite (2010)

Commentationes Mathematicae Universitatis Carolinae

Let R be a 2 -torsion free * -prime ring, d a derivation which commutes with * and J a * -Jordan ideal and a subring of R . In this paper, it is shown that if either d acts as a homomorphism or as an anti-homomorphism on J , then d = 0 or J ⊆ Z ( R ) . Furthermore, an example is given to demonstrate that the * -primeness hypothesis is not superfluous.

On left ( θ , ϕ ) -derivations of prime rings

Mohammad Ashraf (2005)

Archivum Mathematicum

Let R be a 2 -torsion free prime ring. Suppose that θ , φ are automorphisms of R . In the present paper it is established that if R admits a nonzero Jordan left ( θ , θ ) -derivation, then R is commutative. Further, as an application of this resul it is shown that every Jordan left ( θ , θ ) -derivation on R is a left ( θ , θ ) -derivation on R . Finally, in case of an arbitrary prime ring it is proved that if R admits a left ( θ , φ ) -derivation which acts also as a homomorphism (resp. anti-homomorphism) on a nonzero ideal of R , then d = 0 ...

On Lie ideals and Jordan left derivations of prime rings

Mohammad Ashraf, Nadeem-ur-Rehman (2000)

Archivum Mathematicum

Let R be a 2-torsion free prime ring and let U be a Lie ideal of R such that u 2 ∈ U for all u ∈ U . In the present paper it is shown that if d is an additive mappings of R into itself satisfying d ( u 2 ) = 2 u d ( u ) for all u ∈ U , then d ( u v ) = u d ( v ) + v d ( u ) for all u , v ∈ U .

On lifting of idempotents and semiregular endomorphism rings

Tsiu-Kwen Lee, Yiqiang Zhou (2011)

Colloquium Mathematicae

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.

Currently displaying 401 – 420 of 831