For every prime integer p, M. Hochster conjectured the existence of certain p-torsion elements in a local cohomology module over a regular ring of mixed characteristic. We show that Hochster’s conjecture is false. We next construct an example where a local cohomology module over a hypersurface has p-torsion elements for every prime integer p, and consequently has infinitely many associated prim...

An R-module M is called epi-retractable if every submodule of MR is a homomorphic image of M. It is shown that if R is a right perfect ring, then every projective slightly compressible module MR is epi-retractable. If R is a Noetherian ring, then every epi-retractable right R-module has direct sum of uniform submodules. If endomorphism ring of a module MR is von-Neumann regular, then M is semi-...

This is the first paper in a series to study vertex algebra-like objects arising from infinite-dimensional quantum groups (quantum affine algebras and Yangians). In this paper we lay a foundation for this study. We formulate and study notions of quasi module and S-quasi module for a G1-vertex algebra V , where S is a quantum Yang-Baxter operator on V . We also formulate and study a notion of qu...

In this paper we introduce the notions of uniformly quasi-primary ideals and uniformly classical quasi-primary submodules that generalize the concepts of uniformly primary ideals and uniformly classical primary submodules; respectively. Several characterizations of classical quasi-primary and uniformly classical quasi-primary submodules are given. Then we investigate for a ring $R$, when any fi...

We propose two approaches to obtain an isometric embedding of the poloidal Kerr sub-manifold. The first one relies on convex integration process using corrugation from a primitive embedding. This allows us parameter family embeddings reaching limits second consists in consecutive numerical resolutions Gauss-Codazzi-Mainardi and frame equations. method requires geometric assumptions near equator...

Let ΩX be the space of Moore loops on a finite, qconnected, n-dimensional CW complex X , and let R ⊂ Q be a subring containing 1/2. Let ρ(R) be the least non-invertible prime in R. For a graded R-module M of finite type, let FM = M/TorsionM . We show that the inclusion P ⊂ FH∗(ΩX ;R) of the sub-Lie algebra of primitive elements induces an isomorphism of Hopf algebras UP ∼ = −→ FH∗(ΩX ;R), provi...