We provide a new characterization of the notion of sheaf on an étale groupoid G, in terms of a particular kind of Hilbert module on the quantale O(G) of the groupoid. All the theory is developed in the context of the more general class of quantales known as stable quantal frames, of which examples are easy to construct because their category is algebraic. The homomorphisms of our Hilbert module...

RO-algebras are defined and studied. For RO-algebra T , using properties of partial order, it is established that the set of bounded elements can be endowed with C-norm. The structure of commutative subalgebras of T is considered and the Spectral Theorem for any self-adjoint element of T is proven.

Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case. Alizadeh and Goldfarb [Math. Program. Ser. A 95 (2003) 3-51] introduced primal-dual path-following algorithms for solving second-order cone programming problems. In this paper, we generalize their work by using the machinery of Euclidean Jordan alg...

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...

Here G is considered as an algebraic group defined over F . The Lie algebra g may be identified with Mn(F ), with Lie bracket [X,Y ] = XY − Y X . The group T is isomorphic to the algebraic torus Gm, T (F ) is isomorphic to (F), and the Lie algebra t is isomorphic to F. The character group X(T ) is the lattice of algebraic homomorphisms T → Gm, the cocharacter group that of algebraic homomorphis...

Let C be a non-empty class of modules closed under isomorphic copies. We consider some classes of modules associated to C. Among them, we study two important classes in the theory of natural and conatural classes of modules, namely the class consisting of all modules having no non-zero submodule in C, as well as its dual.

orbit closure, 32 character, 33cone, 9dual, 10lattice, 10strongly convex, 10convex function, 42 distinguished point, 28divisorCartier, 38T -invariant, 40principal, 39prime, 37Weil, 37T -invariant, 39principal, 38divisor class group, 38