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 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...

Let $R$ be a commutative ring and let $I$ be an ideal of $R$. In this paper, we will introduce the notions of 2-absorbing $I$-prime and 2-absorbing $I$-second submodules of an $R$-module $M$ as a generalization of 2-absorbing and strongly 2-absorbing second submodules of $M$ and explore some basic properties of these classes of modules.

We investigate perturbative thermodynamic geometry of nonextensive ideal classical, Bose, and Fermi gases. We show that the intrinsic statistical interaction of nonextensive Bose (Fermi) gas is attractive (repulsive) similar to the extensive case but the value of thermodynamic curvature is changed by a nonextensive parameter. In contrary to the extensive ideal classical gas, the nonextensive on...

Given two Banach spaces X and Y , we write L(X, Y ) for the space of all continuous linear operators from X to Y . A linear subspace J of L(X, Y ) is said to be an ideal if ATB ∈ J whenever A ∈ L(Y ), T ∈ J , and B ∈ L(X). It is known (see, e.g., Caradus:74 [CPY74]) that the only norm closed ideal in L(lp), 1 6 p < ∞ is the ideal of compact operators. The structure of closed ideals in L(lp ⊕ lq...

We construct a Banach space Z such that the lattice of closed two-sided ideals of the Banach algebra B(Z) of bounded operators on Z is as follows: {0} ⊂ K (Z) ⊂ E (Z) ⊂ ⊂ M1 M2 ⊂ ⊂ We then determine which kinds of approximate identities (bounded/left/right), if any, each of the four non-trivial closed ideals of B(Z) contains, and we show that the maximal ideal M1 is generated as a left ideal by...

Using linear entropy as a measure of entanglement, we investigate the entanglement generated via a beam splitter using deformed Barut-Girardello coherent states. We show that the degree of entanglement depends strongly on the q-deformation parameter and amplitude Z of the states. We compute the Mandel Q parameter to examine the quantum statistical properties of these coherent states and make a ...

We predict that plutonium hexaboride (PuB(6)) is a strongly correlated topological insulator, with Pu in an intermediate valence state of Pu(2.7+). Within the combination of dynamical mean field theory and density functional theory, we show that PuB(6) is an insulator in the bulk, with nontrivial Z(2) topological invariants. Its metallic surface states have a large Fermi pocket at the X[over ¯]...

the minimal prime decomposition for semiprime ideals is defined and studied on z-ideals of c(x). the necessary and sufficient condition for existence of the minimal prime decomposition of a z-ideal / is given, when / satisfies one of the following conditions: (i) / is an intersection of maximal ideals. (ii) i is an intersection of o , s, when x is basically disconnected. (iii) i=o , when x x ha...