we show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. as aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. this generalizes and simplifies a result of  dung and   smith. as another consequen...

Hodges and Levasseur described the primitive spectra of quantized coordinate rings of SL3 [14], and then of SLn [15]. These results established a close connection between primitive ideals, torus action, and Poisson geometry. The proofs relied on explicit computations involving generators and relations. Subsequently, Joseph generalized the Hodges–Levasseur program to semisimple algebraic quantum...

Strain-free GaAs/Al0.33Ga0.67As quantum rings are fabricated by droplet epitaxy. Both photoresponse and photoluminescence spectra confirm optical transitions in quantum rings, suggesting that droplet epitaxial nanomaterials are applicable to intermediate band solar cells. The effects of post-growth annealing on the quantum ring solar cells are investigated, and the optical properties of the sol...

Generators and relations are given for the subalgebra of cocommutative elements in the quantized coordinate rings O(Gq) of the classical groups, where q is transcendental. This is a ring theoretic formulation of the well known fact that the representation theory of Gq is completely analogous to its classical counterpart. The subalgebras of cocommutative elements in the corresponding FRT-bialgeb...

We study actions of pointed Hopf algebras in the Z-graded setting. Our main result classifies inner-faithful generalized Taft on quantum Weyl which respect Z-grading. also show that generically invariant rings are commutative rings.

Aspects of duality and mirror symmetry in string theory are discussed. We emphasize, through examples, the importance of loop spaces for a deeper understanding of the geometrical origin of dualities in string theory. Moreover we show that mirror symmetry can be reformulated in very simple terms as the statement of equivalence of two classes of topological theories: Topological sigma models and ...

In this paper, the electronic eigenstates and energy spectra of single and two-interacting electrons confined in a concentric double quantum rings with a perpendicular magnetic field in the presence of         on-center donor and acceptor impurities are calculated using the exact diagonalization method. For a single electron case, the binding energy of on-center donor and acceptor impurities ar...

We propose a definition for quantum Fourier transforms in settings where the algebraic structure is that of a finite field, and show that they can be performed efficiently by a quantum computer. Using these finite field quantum Fourier transforms, we obtain the strongest separation between quantum and classical query complexity known to date—specifically, we define a problem that requires Ω(2) ...