In recent years various authors have studied C*-algebras generated by singular integral operators, Wiener-Hopf operators, Toeplitz operators, etc., and representations of these algebras. Analysis in these algebras is accomplished modulo a suitable ideal (usually the commutator and/or compact ideal). A similar procedure is used in the theory of pseudo-differential operators except that the empha...

Let A be the ring obtained by localizing the polynomial ring κ[X, Y, Z, W ] over a field κ at the maximal ideal (X, Y, Z, W) and modulo the ideal (XW − Y Z). Let p be the ideal of A generated by X and Y. We study the module structure of a minimal injective resolution of A/p in details using local cohomology. Applications include the description of Ext i A (M, A/p), where M is a module construct...

we call a module  essentially retractable if homr for all essential submodules n of m. for a right fbn ring r, it is shown that: (i)  a non-zero module  is retractable (in the sense that homr for all non-zero ) if and only if certain factor modules of m are essentially retractable nonsingular modules over r modulo their annihilators. (ii)  a non-zero module  is essentially retractable if and on...

Recently, Andrews introduced the function s(n) = spt(n) which counts the number of smallest parts among the integer partitions of n. We show that its generating function satisfies an identity analogous to Ramanujan's mock theta identities. As a consequence, we are able to completely determine the parity of s(n). Using another type of identity, one based on Hecke operators, we obtain a complete ...

Let A be the ring obtained by localizing the polynomial ring κ[X, Y, Z, W ] over a field κ at the maximal ideal (X, Y, Z, W) and modulo the ideal (XW − Y Z). Let p be the ideal of A generated by X and Y. We study the module structure of a minimal injective resolution of A/p in details using local cohomology. Applications include the description of Ext i A (M, A/p), where M is a module construct...

Let A be the ring obtained by localizing the polynomial ring κ[X,Y, Z,W ] over a field κ at the maximal ideal (X, Y, Z,W ) and modulo the ideal (XW − Y Z). Let p be the ideal of A generated by X and Y . We study the module structure of a minimal injective resolution of A/p in details using local cohomology. Applications include the description of Ext A (M,A/p), where M is a module constructed b...

We prove the following result on the universal localization of a ring R at an ideal I: If the universal localization is flat as an R-module, then R satisfies the Ore condition with respect to the multiplicative set of elements that become invertible modulo I. It is well known that for domains the converse of this result holds, and hence we have found in this case a new characterization of the O...

Consider an elliptic self-adjoint pseudodifferential operator A acting on m-columns of half-densities a closed manifold M, whose principal symbol is assumed to have simple eigenvalues. Relying basis projections commuting with A, we construct almost-unitary that diagonalizes modulo infinitely smoothing operator. We provide invariant algorithm for the computation its full symbol, as well explicit...