Let H be a bialgebra and D an H-bimodule algebra and H-bicomodule coalgebra. We find sufficient conditions on D for the L-R-smash product algebra and coalgebra structures on D ⊗ H to form a bialgebra (in this case we say that (H,D) is an L-R-admissible pair), called L-R-smash biproduct. The Radford biproduct is a particular case, and so is, up to isomorphism, a double biproduct with trivial pai...

Abstract The rank 1 bosonic ghost vertex algebra, also known as the $$\beta \gamma $$ ? ? ghosts, symplectic bosons or Weyl is a simple example of conformal field theory which neither rational, nor $$C_2$$ C 2 -co...

It has long been recognized that the development of a theory of ring and module spectra, which bears the same relationship to the category of spectra as the ordinary theory of rings and modules does to the category of abelian groups, is a very desirable thing. A number of such theories exist. The different approaches [12] and [15] solve the problem in a satisfactory way, and more recently (see ...

Methods from homological algebra [16] play a more and more important role in the study of multidimensional linear systems [15], [14], [6]. The use of modules allows an algebraic treatment of linear systems which is independent of their presentations by systems of equations. The type of linear system (ordinary/partial differential equations, timedelay systems, discrete systems. . . ) is encoded ...

Controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator on abstract Hilbert spaces. Fusion frames and g-frames generalize frames. Hilbert C*-modules form a wide category between Hilbert spaces and Banach spaces. Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*...

We first study some properties‎ ‎of $A$-module homomorphisms $theta:Xrightarrow Y$‎, ‎where $X$‎ ‎and $Y$ are Fréchet $A$-modules and $A$ is a unital‎ ‎Fréchet algebra‎. ‎Then we show that if there exists a‎ ‎continued bisection of the identity for $A$‎, ‎then $theta$ is‎ ‎automatically continuous under certain condition on $X$‎. ‎In‎ ‎particular‎, ‎every homomorphism from $A$ into certain‎ ‎Fr...

Let A be a ring and MA the category of right A-modules. It is well known in module theory that any A-bimodule B is an A-ring if and only if the functor − ⊗A B : MA → MA is a monad (or triple). Similarly, an A-bimodule C is an A-coring provided the functor − ⊗A C : MA → MA is a comonad (or cotriple). The related categories of modules (or algebras) of −⊗A B and comodules (or coalgebras) of − ⊗A C...