We introduce the notion of support equivalence for (co)module algebras (over Hopf algebras), which generalizes in a natural way (weak) gradings. show that each class algebra structures on given A, there exists unique universal H together with an H-(co)module structure A such any other equivalent factors through action H. study and mentioned above group gradings, Hopf-Galois extensions, actions ...

We show that the support of a simple weight module over the Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all non-trivial weight spaces of such module are infinite dimensional. As a corollary we obtain that every simple weight module over the Virasoro algebra, having a nontrivial finite-dimensional weight space, is a Harish-Chandra ...

Factor H is a regulatory glycoprotein of the complement system. We expressed the three N-terminal complement control protein modules of human factor H (FH1-3) and confirmed FH1-3 to be the minimal unit with cofactor activity for C3b proteolysis by factor I. We reconstructed FH1-3 from NMR-derived structures of FH1-2 and FH2-3 revealing an approximately 105-A-long rod-like arrangement of the mod...

We introduce the notion of idempotent radical class of module coalgebras over a bialgebra B. We prove that if R is an idempotent radical class of B-module coalgebras, then every B-module coalgebra contains a unique maximal B-submodule coalgebra in R. Moreover, a B-module coalgebra C is a member of R if, and only if, DB is in R for every simple subcoalgebra D of C. The collection of B-cocleft co...

we state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. in particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. also we show that if m is an strong comultiplicati...

The LTPP program acknowledges that weigh-in-motion (WIM) and automatic vehicle classification (AVC) are not mature technologies. As such, participating agency and site-specific conditions may legitimately warrant the use of procedures other than those presented below. In addition, LTPP recognizes that participating agencies use a variety of types of traffic data collection equipment and have di...

Let $R$ be a commutative Noetherian ring with non-zero identity, $\mathfrak{a}$ an ideal of $R$, $M$ finitely generated $R$--module, and $X$ arbitrary $R$--module. In this paper, for non-negative integers $s, t$ $R$--module $N$, we study the membership $\operatorname{Ext}_{R}^{s}(N, \operatorname{H}^{t}_{\mathfrak{a}}(M, X))$ in Serre subcategories category $R$--modules present some upper bound...