By an F -semi-linear G-representation we mean an F -space V with a (k-linear) G-action such that (a v) = a v for any 2 G, v 2 V and a 2 F . This is the same as a module over the algebra F hGi := F ZZ[G] with evident action of F and the diagonal action of G. If G acts on F faithfully, then F hGi is a central k-algebra. Semi-linear G-representations nite-dimensional over F form an abelian tensor ...

Background: Misinformation and disinformation perpetuate negative stereotypes, reinforce prejudice lead to racially motivated discrimination. As displayed in post-secondary institutions worldwide, white-centric perspectives are primarily embedded school cultures systems. Such racial aggressions produce ‘racial battle fatigue,’ creating physiological, behavioural stress for the recipient. Virtua...

We characterize the initial terms under a diagonal term order of the supersymmetric Schur/Weyl module S(V V ) associated to a row-convex shape D. We show the biwords corresponding to the initial terms of S are closed under dual-Knuth equivalence and that the recording tableaux for these words are decomposable in the sense of [10]. We consider the natural action of bases of S in which the elemen...

By a coalgebra over the commutative ring K or a K-coalgebra, we understand a cocommutative, coassociative K-coalgebra with counit. More explicitly we mean a K-module C equipped with maps &C+C&C, subject to the requirement (where we write @ for OK) that the following diagrams commute: CLC@C where the vertical arrow is the one which switches the factors; CAC@C 1 CC38 C@C e@'CtC@C@C, where we have...

a module $m$ is called $emph{h}$-cofinitely supplemented if for every cofinite submodule $e$ (i.e. $m/e$ is finitely generated) of $m$ there exists a direct summand $d$ of $m$ such that $m = e + x$ holds if and only if $m = d + x$, for every submodule $x$ of $m$. in this paper we study factors, direct summands and direct sums of $emph{h}$-cofinitely supplemented modules. let $m$ be an $emph{h}$...

The research objective of this essay is integrating multi agent systems (MAS) into networked 3D virtual learning environments (VLE). Integrating a multi agent system with a 3D virtual learning environment allows abstracting from the peculiarities of interacting with the virtual environment, so designers may focus on the pedagogical problem to solve. The focus of this research is specifically on...

Higher education courses are increasingly created as student organized collections of interrelated modules. At the same time, frequent change of subject matter and knowledge in its background must be handled. Above and other factors created and recognized a need for efficient computer based course management. Conventional computer aided teaching methods are not suitable to organize, manage, and...