In this paper we show that in a homological category in the sense of F. Borceux and D. Bourn, the notion of an internal precrossed module corresponding to a star-multiplicative graph, in the sense of G. Janelidze, can be obtained by directly internalizing the usual axioms of a crossed module, via equivariance. We then exhibit some sufficient conditions on a homological category under which this...

we show that  higher derivations on a hilbert$c^{*}-$module associated with the cauchy functional equation satisfying generalized hyers--ulam stability.

in this work we deal with actions of vector groupoid which is a new concept in the literature‎. ‎after we give the definition of the action of a vector groupoid on a vector space‎, ‎we obtain some results related to actions of vector groupoids‎. ‎we also apply some characterizations of the category and groupoid theory to vector groupoids‎. ‎as the second part of the work‎, ‎we define the notion...

Using free simplicial groups, it is shown how to construct a free or totally free 2-crossed module on suitable construction data. 2-crossed complexes are introduced and similar freeness results for these are discussed.

Using free simplicial groups, it is shown how to construct a free or totally free 2-crossed module on suitable construction data. 2-crossed complexes are introduced and similar freeness results for these are discussed.

We prove, under some mild conditions, that the equivariant twisted K-theory group of a crossed module admits a ring structure if the twisting 2-cocycle is 2multiplicative. We also give an explicit construction of the transgression map T1 : H ∗(Γ • ;A) → H((N ⋊ Γ) • ;A) for any crossed module N → Γ and prove that any element in the image is ∞-multiplicative. As a consequence, we prove that, unde...

Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...

the generalized principal ideal theorem is one of the cornerstones of dimension theory for noetherian rings. for an r-module m, we identify certain submodules of m that play a role analogous to that of prime ideals in the ring r. using this definition, we extend the generalized principal ideal theorem to modules.

We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.  

In this paper, applying the concept of generalized A-valued norm on a right $H^*$-module and also the notion of ϕ-homomorphism of Finsler modules over $C^*$-algebras we first improve the definition of the Finsler module over $H^*$-algebra and then define ϕ-morphism of Finsler modules over $H^*$-algebras. Finally we present some results concerning these new ones.