1. Amitsur in his paper on Finite Dimensional Central Division Algebras [l] has proved that in a division ring D with center C, (P: C) 5= ra2 < =o if and only if every primitive homomorphic image of a polynomial ring P[x] is a complete matrix ring Ah, h^n, over a division ring A. Equivalently speaking, a division ring is finite dimensional over its center if and only if the polynomial ring over...

It is well-known that for several natural decision problems no budget balanced Groves mechanisms exist. This has motivated recent research on designing variants of feasible Groves mechanisms (termed as ‘redistribution of VCG (Vickrey-Clarke-Groves) payments’) that generate reduced deficit. With this in mind, we study sequential pivotal mechanisms and consider optimal strategies that can lower t...