The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...

This article presents a novel adaptive bilateral control scheme for obtaining ideal responses for teleoperation systems with uncertainties. A condition that is equivalent to getting an ideal response in teleoperation has been found to be making the closed-loop dynamics of master and slave manipulators a similar form. An adaptive approach is applied to achieve similarity for the uncertain master...

In the paper we generalize a fibre criterion for a polynomial f to belong to a primary ideal I in the polynomial ring K[X, Y ]. We also investigate the general case where the ideal I is not primary. Let {X1, . . . , Xn} be any set of variables. We shall write K[X] instead of K[X1, . . . , Xn]. If f ∈ K[X,Y ], where X and Y are sets of variables, K is an algebraically closed field, Y = {Y1, . . ...