We introduce the notion of 'bar category' by which we mean a monoidal category equipped with additional structure induced by complex conjugation. Examples of our theory include bimodules over a *-algebra, modules over a conventional Hopf *-algebra and modules over a more general object which call a 'quasi-*-Hopf algebra' and for which examples include the standard quantum groups u q (g) at q a ...

In this work we develop some aspects of the theory of Hopf algebras to the context of autonomous map pseudomonoids. We concentrate in the Hopf modules and the Centre or Drinfel’d double. If A is a map pseudomonoid in a monoidal bicategory M , the analogue of the category of Hopf modules for A is an Eilenberg-Moore construction for a certain monad in Hom(M op,Cat). We study the existence of the ...

Python is an extensible, interpreted, object-oriented programming language. It supports a wide range of applications, from simple text processing scripts to interactive WWW browsers. While the Python Reference Manual describes the exact syntax and semantics of the language, it does not describe the standard library that is distributed with the language, and which greatly enhances its immediate ...

This theorem, already known for finitely generated projective modules[l, I, Proposition 6.1], has been recently proved for arbitrary projective modules over commutative semi-hereditary rings by I. Kaplansky [2], who raised the problem of extending it to the noncommutative case. We recall two results due to Kaplansky: Any projective module (over an arbitrary ring) is a direct sum of countably ge...

‎we introduce a generalization of the notion of‎ depth of an ideal on a module by applying the concept of‎ local cohomology modules with respect to a pair‎ ‎of ideals‎. ‎we also introduce the concept of $(i,j)$-cohen--macaulay modules as a generalization of concept of cohen--macaulay modules‎. ‎these kind of modules are different from cohen--macaulay modules‎, as an example shows‎. ‎also an art...

Smartphones and tablets have become an integral part of our daily life. They increasingly store and process security and privacy sensitive data which makes them attractive targets for attackers. In particular for the popular Android OS, a number of security extensions have been proposed that target specific security and privacy problems caused by Android’s lack of a fine-grained, dynamic and sy...

In oorplanning it is common that a designer wants to have certain modules abutting with one another in the nal pack ing Unfortunately few oorplanning algorithm can han dle abutment constraints although this feature is useful in practice The problem of controlling the relative positions of an arbitrary number of modules is non trivial Slicing oorplans have an advantageous feature that the topolo...

The treatment of photovoltaic (PV) waste is gaining traction the world over, with recovery valuable materials from end-of-life , or damaged and out-of-spec polycrystalline silicon PV modules. These are a focus recycling. However, current recycling practices usually involve excessive damage to cells that could otherwise be reused if recovered undamaged. ability recover undamaged cells, capable r...

‎Highest weight modules of the double affine Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎Singular vectors of Verma modules are‎ ‎determined using a similar condition with horizontal affine Lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

This paper is concerned with the relation between local cohomology modules defined by a pair of ideals and the Serre subcategories of the category of modules. We characterize the membership of local cohomology modules in a certain Serre subcategory from lower range or upper range.