We show that the associated form, or, equivalently, a Macaulay inverse system, of an Artinian complete intersection of type (d, . . . , d) is polystable. As an application, we obtain an invariant-theoretic variant of the Mather-Yau theorem for homogeneous hypersurface singularities.

Characterizations of fuzzy ideals of a pseudo-BCH-algebra are established. Conditions for a fuzzy set to be a fuzzy ideal are given. The homomorphic properties of fuzzy ideals are provided. Finally, characterizations of Noetherian pseudo-BCH-algebras and Artinian pseudoBCH-algebras via fuzzy ideals are obtained. Mathematics Subject Classi…cation: 03G25, 06F35.

Under the assumption that a residually finite-dimensional Hopf algebra H has an Artinian ring of fractions, it is proved flat module over any right coideal subalgebra satisfying polynomial identity and faithfully subalgebra. As consequence we find large class algebras which are all subalgebras subalgebras.

Let R be a local Noetherian commutative ring. We prove that is an Artinian Gorenstein ring if and only every ideal in trace ideal. discuss when the of module coincides with its double annihilator.

In this paper we consider Artinian modules over power series rings endowed with a Frobenius map. We describe a method for finding the set of all prime annihilators of submodules which are preserved by the given Frobenius map and on which the Frobenius map is not nilpotent. This extends the algorithm by Karl Schwede and the first author, which solved this problem for submodules of the injective ...

Let S denote the graded polynomial ring C[x1, . . . , xm]. We interpret a chain complex of free S-modules having artinian homology as an S1-equivariant map Cm \ {0} → X, where X is a moduli space of exact sequences. We obtain cohomological obstructions to such maps, most notably a completely new derivation of Herzog-Kühl-type equations for chain complexes. CONTENTS

In this paper, considering the difference between the finiteness dimension and cohomological dimension for a finitely generated module, we investigate the asymptotic behavior of grades of components of graded local cohomology modules with respect to irrelevant ideal; as long as we study some artinian and tameness property of such modules.

Let Λ be a left-artinian ring. Generalizing the Loewy length, we propose the layer length associated with a torsion theory, which is a new measure for finitely generated Λ-modules. As an application, we obtain a theorem having as corollaries the main results of [3] and [7].