Abstract We develop filtered-graded techniques for algebras in monoidal categories with the main goal of establishing a categorical version Bongale’s 1967 result: filtered deformation Frobenius algebra over field is as well. Toward goal, we first construct associated graded functor, building on prior works Ardizzoni and Menini, Galatius et al., Gwillian Pavlov. Next, produce equivalent conditio...

La filtration canonique par les pentes d'un module aux q-différences et le gradué associé. Résumé Nous montrons que le polygone de Newton d'uné equation aux q-différences linéaire ne dépend que du module aux q-différences correspondant. Nous interprétons les classiques résultats de factorisation convergente de Adams-Birkhoff-Guenther en termes d'existence d'une filtration canonique par les pent...

Let G be a pro nite group. We de ne an S[[G]]-module to be a G-spectrum X that satis es certain conditions, and, given an S[[G]]-module X, we de ne the homotopy orbit spectrum XhG. When G is countably based and X satis es a certain niteness condition, we construct a homotopy orbit spectral sequence whose E2-term is the continuous homology of G with coefcients in the graded pro nite b Z[[G]]-mod...

Our goal in this paper is to define a version of Hochschild homology and cohomology suitable for a class of algebras admitting compatible actions of bialgebras, called “module algebras” (Definition 2.1). Our motivation lies in the following problem: for an algebra A which admits a module structure over an arbitrary bialgebra B compatible with its product structure, the Hochschild or the cyclic ...

Let (R;m) be a Noetherian local ring and let I be an R-ideal. The associated graded ring of I, G = grI(R), plays a significant role in the study of resolution of singularities. Its relevance lies upon the fact that it represents algebraically the exceptional fiber of the blowup of a variety along a subvariety. A commonly addressed issue is to find numerical conditions that imply lower bounds on...

let x be a hypergroup. in this paper, we study the homomorphisms on certain subspaces of l(x)* which are weak*-weak* continuous.

We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated by toric geometry, we work with modules over a polynomial ring graded by a finitely generated abelian group. As in the standard graded case, our definition of multigraded regularity involves the vanishing of graded components of local cohomology. We establish the key properties of regularity: its connection with the m...

The Hilbert functions and the regularity of the graded components of local cohomology of a bigraded algebra are considered. Explicit bounds for these invariants are obtained for bigraded hypersurface rings. Introduction In this paper we study algebraic properties of the graded components of local cohomology of a bigradedK-algebra. Let P0 be a Noetherian ring, P = P0[y1, . . . , yn] be the polyn...