let $r$ be a commutative noetherian ring with non-zero identity, $fa$ an ideal of $r$, and $x$ an $r$--module. here, for fixed integers $s, t$ and a finite $fa$--torsion $r$--module $n$, we first study the membership of $ext^{s+t}_{r}(n, x)$ and $ext^{s}_{r}(n, h^{t}_{fa}(x))$ in the serre subcategories of the category of $r$--modules. then, we present some conditions which ensure the exi...

We extend our work in [1] to the case of Hopf comodule coalgebras. We introduce the cocylindrical module C♮H, where H is a Hopf algebra with bijective antipode and C is a Hopf comodule coalgebra over H. We show that there exists an isomorphism between the cocyclic module of the crossed coproduct coalgebra C>◭H and ∆(C♮H), the cocyclic module related to the diagonal of C♮H. We approximate HC(C >...

In this paper we proved that every g-Riesz basis for Hilbert space $H$ with respect to $K$ by adding a condition is a Riesz basis for Hilbert $B(K)$-module $B(H,K)$. This is an extension of [A. Askarizadeh, M. A. Dehghan, {em G-frames as special frames}, Turk. J. Math., 35, (2011) 1-11]. Also, we derived similar results for g-orthonormal and orthogonal bases. Some relationships between dual fra...

neurite outgrowth from dorsal root ganglion (drg) explants is a method of evaluating neurotrophic activity of growth factors. when complete medium containing collagen was supplemented with nerve growth factor (ngf) drg outgrowth was observed after 18 h. in the absence of ngf and in the presence of collagen, the drg outgrowth took place after 72 h. in wells not supplemented with collagen gel in ...

This paper proves: Let F be a saturated formation containing U . Suppose that G is a group with a normal subgroup H such that G/H ∈ F . (1) If all maximal subgroups of any Sylow subgroup of F ∗(H) are c-supplemented in G, then G ∈ F ; (2) If all minimal subgroups and all cyclic subgroups with order 4 of F ∗(H) are c-supplemented in G, then G ∈ F .

Neurite outgrowth from dorsal root ganglion (DRG) explants is a method of evaluating neurotrophic activity of growth factors. When complete medium containing collagen was supplemented with nerve growth factor (NGF) DRG outgrowth was observed after 18 h. In the absence of NGF and in the presence of collagen, the DRG outgrowth took place after 72 h. In wells not supplemented with collagen gel in ...

The cohomology of a group G with coefficients in a left G–module M is denoted H .GIM /. We are primarily interested in the case where M is the group ring, ZG . Since ZG is a G–bimodule, H .GIZG/ inherits the structure of a right G– module. When G is discrete and acts properly and cocompactly on a contractible CW complex , there is a natural topological interpretation for this cohomology group:...