In this short note, we construct a right adjoint to the functor which associates ring R equipped with group action its twisted ring. This admits an interpretation as semilinearization, in that it sends R-module of semilinear automorphisms module. As immediate corollary, provide novel proof classical observation modules over are base together action.

This article introduces our research efforts to build the Essex Rovers’01 robot soccer team participated in the RoboCup-2001 competition. A modular design for implementing a behavior-based hierarchy is introduced, which consists of three modules such as Perception module, Cognition module and Action module. This architecture is used for the team to achieve intelligent actions in real time. The ...

A finite module M over a noetherian local ring R is said to be Gorenstein if Ext(k, M) = 0 for all i 6= dimR. A endomorphism φ : R → R of rings is called contracting if φ(m) ⊆ m for some i ≥ 1. Letting R denote the R-module R with action induced by φ, we prove: A finite R-module M is Gorenstein if and only if HomR( R,M) ∼= M and ExtiR( R,M) = 0 for 1 ≤ i ≤ depthR.

This paper addresses the issue of hybridization between reactive and cognitive approaches within a single decision-making architecture for virtual agent in an urban simulation. We use a reactive module in order to manage reactive behaviors and agent autonomy, and a cognitive module for anticipation, learning and complex behaviors management. The purpose of the cognitive module is to increase th...

Every simple module having character height at most one for a restricted Cartantype Lie algebra g can be realized as a quotient of a module obtained by starting with a simple module S for the homogeneous component of degree zero in the natural grading of g, extending the action trivially to positive components and inducing up to g. It is shown that if S is not restricted, or if it is restricted...

This paper presents the rudiments of Hilbert-Mumford Intersection (HMI) theory: intersection theory on the relative Hilbert scheme of a family of nodal (or smooth) curves, over a base of arbitrary dimension. We introduce an additive group of geometric cycles, called ’tautological module’, generated by diagonal loci, node scrolls, and twists thereof. We determine recursively the intersection act...

we state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. in particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. also we show that if m is an strong comultiplicati...

We prove that an arbitrary (not necessarily countably generated) Hilbert G −A module on a G − C∗ algebra A admits an equivariant embedding into a trivial G−A module, provided G is a compact Lie group and its action on A is ergodic.