Exploring further the connection between exponentiation on real closed fields and existence of an integer part modelling strong fragments arithmetic, we demonstrate that each model true arithmetic is exponential field elementarily equivalent to numbers with Peano a admits isomorphism its ordered additive multiplicative group positive elements. Under assumption Schanuel’s Conjecture, obtain stre...

Our goal will be to find subsets of Zm that form groups under the operation of multiplication modulo m. By utilizing the isomorphism Zm ∼= Zn ⊕ Zk, we will find multiplicative groups contained in Zn ⊕ Zk and then map these back to Zm. In particular, if m = nk with gcd(n, k) = 1, our objective is to find particular multiplicative subsets of Zn × Zk that are groups and whose first coordinate is a...

The purpose of this paper is to study conditions under which the restriction of a certain Galois connection on a complete lattice yields an isomorphism from a set of prime elements to a set of coprime elements. An important part of our study involves the set on which the way-below relation is multiplicative.

The structure of the group of quasi multiplicative arithmetical functions such that f(1) 6=0 with respect to Dirichlet and the more general Davison convolution via an isomorphism to a subgroup of upper triangular and Toeplitz matrices will be described. AMS Classification Number: 11A25

We introduce an extension of continuous wavelet theory that enables efficient implementation multiplicative operators in the coefficient space. In new theory, signal space is embedded a larger abstract – so called window–signal There canonical transform to isometric isomorphism between and Hence, framework wavelet-Plancherel extended transform. Since isomorphism, any operation can be pulled-bac...

Let G be a commutative affine algebraic group over field F, and let H:FieldsF→AbGrps functor. A (homomorphic) H-invariant of is natural transformation Tors(−,G)→H, where Tors(−,G) the functor FieldsF→AbGrps taking extension L/F to isomorphism classes GL-torsors Spec(L). The goal this paper compute Invhom1(G,H) H-invariants when multiplicative type, H L×⊗ZQ/Z.

We construct a map ζ from K0(P) to (Z[x]/xd+1)× × Z, where (Z[x]/xd+1)× is a multiplicative Abelian group with identity 1, and show that ζ induces an isomorphism between K0(P) and its image. This is inspired by a correspondence between Chern and Hilbert polynomials stated in Eisenbud [1, Exercise 19.18]. The equivalence of these two polynomials over Pd is discussed in this paper.

Exploring further the connection between exponentiation on real closed fields and the existence of an integer part modelling strong fragments of arithmetic, we demonstrate that each model of true arithmetic is an integer part of an exponential real closed field that is elementary equivalent to the reals with exponentiation and that each model of Peano arithmetic is an integer part of a real clo...

We establish a generalization of Breen’s theory of cubic structures on line bundles over group schemes. We study such “n-cubic structures” inductively using multiextensions. As a result we obtain information on the set of isomorphism classes of line bundles with n-cubic structures over finite multiplicative group schemes over Spec (Z) by relating this set to certain corresponding eigenspaces of...

We show that the operation of taking generic extensions provides the set of isomorphism classes of representations of a quiver of Dynkin type with a monoid structure. Its monoid ring is isomorphic to the specialization at q = 0 of Ringel’s Hall algebra. This provides the latter algebra with a multiplicatively closed basis. Using a crystal-type basis for a two-parameter quantum group, this multi...