‎Let $mathcal A$ and $mathcal B$ be unital rings‎, ‎and $mathcal M$‎ ‎be an $(mathcal A‎, ‎mathcal B)$-bimodule‎, ‎which is faithful as a‎ ‎left $mathcal A$-module and also as a right $mathcal B$-module‎. ‎Let ${mathcal U}=mbox{rm Tri}(mathcal A‎, ‎mathcal M‎, ‎mathcal‎ ‎B)$ be the triangular ring and ${mathcal Z}({mathcal U})$ its‎ ‎center‎. ‎Assume that $f:{mathcal U}rightarrow{mathcal U}$ is...

We prove that each almost local-global semihereditary ring R has the stacked bases property and is almost Bézout. More precisely, if M is a finitely presented module, its torsion part tM is a direct sum of cyclic modules where the family of annihilators is an ascending chain of invertible ideals. These ideals are invariants of M. Moreover M/tM is a projective module which is isomorphic to a dir...

We prove that each almost local-global semihereditary ring R has the stacked bases property and is almost Bézout. More precisely, if M is a finitely presented module, its torsion part tM is a direct sum of cyclic modules where the family of annihilators is an ascending chain of invertible ideals. These ideals are invariants of M . Moreover M/tM is a projective module which is isomorphic to a di...

We examine actions of finite-dimensional pointed Hopf algebras on central simple division in characteristic 0. (By a action we mean module algebra structure.) In all examples considered, show that the given does admit faithful algebra, and construct such algebra. This is contrast to earlier work Etingof Walton, which it was shown most do not fields. consider bosonizations Nichols finite Cartan ...

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fait...

Introduction. Let F be a field and let V be a finite dimensional vector space over F which is also a module over the ring F[a]. Here a may lie in any extension ring of F. We do not assume, as yet, that V is a faithful module, so that a need not be a linear transformation on V. It is known that by means of a decomposition of V into cyclic F[a]-modules we may obtain a definition of the characteri...

The processing pipeline of a digital camera converts the RAW image acquired by the sensor to a representation of the original scene that should be as faithful as possible. There are mainly two modules responsible for the color-rendering accuracy of a digital camera: the former is the illuminant estimation and correction module, and the latter is the color matrix transformation aimed to adapt th...