Generalized frames are an extension of frames in Hilbert  spaces and  Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an or...

let r be a ring,  be an endomorphism of r and mr be a -rigid module. amodule mr is called quasi-baer if the right annihilator of a principal submodule of r isgenerated by an idempotent. it is shown that an r-module mr is a quasi-baer module if andonly if m[[x]] is a quasi-baer module over the skew power series ring r[[x; ]].

Studied are the moduli spaces of Yang-Mills connections on finitely generated projective modules associated with noncommutative flows. It is actually shown that they are homeomorphic to those on dual modules associated with dual noncommutative flows. Moreover the method is also applicable to the case of noncommutative multi-flows. As an important application, computed are the the moduli spaces ...

An analogue of the Fourier transform is developed for D-algebras. G. Laumon’s equivalence between the derived category of D-modules on an abelian variety and the derived category of O-modules on the universal extension of the dual variety is seen as a degenerate case of a duality for twisted differential operators (tdo’s) with respect to which the dual of a generic tdo is again a tdo.

Let G be a finite group and let k be a field of characteristic p. It is known that a kG-module V carries a non-degenerate G-invariant bilinear form b if and only if V is self-dual. We show that whenever a Morita bimodule M which induces an equivalence between two blocks B(kG) and B(kH) of group algebras kG and kH is self-dual then the correspondence preserves self-duality. Even more, if the bil...

In a previous paper we introduce the concept of full d-stability, in this work several types of generalizations were introduced ; minimal (maximal) d-stable; fully pseudo d-stable and afd-stable module. A dual to the notion of terse module is, also, introduced namely d-terse and it is shown that it is coincide with fully pseudo d-stable.