A rational Mackey functor M for a compact Lie group G can be viewed as a collection of sheaves on spaces of conjugacy classes of subgroups, one for each closed subgroup H, related by restriction maps only. This in turn may be speciied by giving a suitably continuous family consisting of a Q 0 (W G (H))-module V (H) for each closed subgroup H with restriction maps V (^ K) ?! V (K) whenever K is ...

The classical Ritt’s Theorems state several properties of univariate polynomial decomposition. In this paper we present new counterexamples to the first Ritt theorem, which states the equality of length of decomposition chains of a polynomial, in the case of rational functions. Namely, we provide an explicit example of a rational function with coefficients in Q and two decompositions of differe...

 The Mordell-Weil theorem states that the group of rational points‎ ‎on an elliptic curve over the rational numbers is a finitely‎ ‎generated abelian group‎. ‎In our previous paper, H‎. ‎Daghigh‎, ‎and S‎. ‎Didari‎, On the elliptic curves of the form $ y^2=x^3-3px$‎, ‎‎Bull‎. ‎Iranian Math‎. ‎Soc‎.‎‎ 40 (2014)‎, no‎. ‎5‎, ‎1119--1133‎.‎, ‎using Selmer groups‎, ‎we have shown that for a prime $p...

It is shown that the existential theory of G with rational constraints, over an HNN-extension G = 〈H, t; tat = φ(a)(a ∈ A)〉 is decidable, provided that the same problem is decidable in the base group H and that A is a finite group. The positive theory of G is decidable, provided that the existential positive theory of G is decidable and that A and φ(A) are proper subgroups of the base group H w...

Let X be a normal projective variety admitting an action of a semisimple group with a unique closed orbit. We construct finitely many rational curves in X , all having a common point, such that every effective one–cycle on X is rationally equivalent to a unique linear combination of these curves with non–negative rational coefficients. When X is nonsingular, these curves are projective lines, a...

Abstract. We show that the Strong Novikov Conjecture for the maximal C∗-algebra C∗(π) of a discrete group π is equivalent to a statement in topological K-theory for which the corresponding statement in algebraic K-theory is always true. We also show that for any group π , rational injectivity of the full assembly map for K ∗(C ∗(π)) follows from rational injectivity of the restricted assembly map.

We examine the cokernel of canonical homomorphism from trivial source ring a finite group to $p$-rational complex characters. use Boltje and Co\c{s}kun's theory fibered biset functors determine structure cokernel. An essential tool in determination this is Bouc's rational $p$-biset functors.

A rational function R(x, y) over a field is said to be associative if R(R(x, y), z) = R(x,R(y, z)). Associative rational functions over a field define group laws on subsets of the field (plus the point at infinity). In this paper, all the associative rational functions of two variables over an arbitrary field are determined and consequently all the groups obtainable from such functions are dete...