We address the problem of enumerating all models of Boolean formulæ in order of non-decreasing weight in Schaefer’s framework. The weight of a model is the number of variables assigned to 1. Tractability in this context amounts to enumerating all models one after the other in sorted order, with polynomial delay between two successive outputs. The question of model-enumeration has already been s...

Abstract In this article, we establish a motivic analog of an enumeration result James–Thomas [ 28] on non-stable vector bundles in topological setting. Using this, obtain results projective modules rank $d$ over smooth affine $k$-algebra $A$ dimension $d$, recovering particular Suslin and Bhatwadekar cancellation such bundles. Admitting conjecture Asok Fasel, prove $d-1$ if the base field $k$ ...

A finite ring with an identity whose lattice of ideals forms a unique chain is called ring. Let R be commutative invariants p,n,r,k,m. It known that Eisenstein extension degree k Galois S=GR(pn,r). If p−1 does not divide k, the structure unit group U(R) known. The case (p−1)∣k was partially considered by M. Luis (1991) providing counterexamples demonstrated results Ayoub failed to capture direc...