A variational inequality for the images of k-dimensional hyper-planes under quasiconformal maps of the n-dimensional Euclidean space is proved when 1 ≤ k ≤ n − 2 .

The foldness of PI( , , ⊆)BCK -ideals and PI(⊆, ⊆, ⊆)BCK -ideals is considered, and their properties are investigated. Hyper homomorphic inverse image of PI( , , ⊆)BCK -ideals, PI( , ⊆, ⊆)BCK -ideals, PI(⊆, ⊆, ⊆)BCK -ideals, and PI( , , )BCK -ideals are discussed.

In this document we make good on all the assertions we made in the previous paper " Moduli spaces of commutative ring spectra " [20] wherein we laid out a theory a moduli spaces and problems for the existence and uniqueness of E ∞-ring spectra. In that paper, we discussed the the Hopkins-Miller theorem on the Lubin-Tate or Morava spectra E n ; in particular, we showed how to prove that the modu...

In this paper, we introduce the concepts of right, left and product stabilizers on hoops and study some properties and the relation between them.  And we try to find that how they can be equal and investigate that under what condition they can be filter, implicative filter, fantastic and positive implicative filter. Also, we prove that  right and product stabilizers are filters and if they are ...

This is a further investigation of our approach to group actions in homological algebra the settings homology $$\Gamma $$ -simplicial groups, particularly -equivariant and cohomology -groups. new direction called -homological algebra. The abstract kernel non-abelian extensions its relationship with obstruction theory, second are extended case -extensions We compute rational (co)homology groups ...

Let K be an infinite field and K〈X〉 = K〈X1, ..., Xn〉 the free associative algebra generated by X = {X1, ..., Xn} over K. It is proved that if I is a two-sided ideal of K〈X〉 such that the K-algebra A = K〈X〉/I is almost commutative in the sense of [3], namely, with respect to its standard N-filtration FA, the associated N-graded algebra G(A) is commutative, then I is generated by a finite Gröbner...

In this article, we define a non-commutative deformation of the ”symplectic invariants” (introduced in [13]) of an algebraic hyperelliptical plane curve. The necessary condition for our definition to make sense is a Bethe ansatz. The commutative limit reduces to the symplectic invariants, i.e. algebraic geometry, and thus we define non-commutative deformations of some algebraic geometry quantit...

In this paper we study a 3-fold X ⊂ P that is a complete intersection of two hypersurfaces Fn and Gk such that n ≥ k and the only singularities of X are ordinary double points. The 3-fold X is called factorial if every surface in X is cut by a hypersurface in P. The factoriality of the 3-fold X is equivalent to a global topological condition rkH4(X,Z) = 1, which follows from the Lefschetz theor...

We discuss two versions of a conjecture attributed to M Barr The Harrison cohomology of a commutative algebra is known to coincide with the Andr e Quillen cohomology over a eld of characteristic zero but not in prime characteristics The conjecture is that a modi ed version of Harrison cohomology taking into account torsion always agrees with Andr e Quillen cohomology We give a counterexample De...