We study Kloosterman sums in a generalized ring-theoretic context, that of finite commutative Frobenius rings. prove number identities for twisted sums, loosely clustered around moment computations.

A Lie version of Turaev’s G-Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a g-quasi-Frobenius Lie algebra for g a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra (q, β) together with a left g-module structure which acts on q via derivations and for which β is g-inva...

Müller generalized in [12] the notion of a Frobenius extension to left (right) quasi-Frobenius extension and proved the endomorphism ring theorem for these extensions. Recently, Guo observed in [9] that for a ring homomorphism φ : R → S, the restriction of scalars functor has to induction functor S ⊗R − : RM → SM as right ”quasi” adjoint if and only if φ is a left quasi-Frobenius extension. In ...

We generalize and prove a hypothesis by V. Arnold on the parity of Frobenius number. For the case of symmetric semigroups with three generators of Frobenius numbers we found an exact formula, which in a sense is the sum of two Sylvester’s formulaes. We prove that the fraction of the symmetric semigroups is vanishing in the weak limit. 1. Definitions Take n mutually prime numbers a1, a2, ..., an...

This article is divided into two parts. In the first part we work over a field k and prove that Frobenius space associated to algebra generated as left A-module by coproduct. particular, dimension coincides with of algebra. second commutative ring We introduce concept nearly algebras in this context construct solutions quantum Yang-Baxter equation starting from elements space. Also, give an alt...

in this note we characterize the compact weighted frobenius-perron operator $p$ on $l^1(sigma)$ and determine their spectra. we also show that every weakly compact weighted frobenius-perron operator on $l^1(sigma)$ is compact.

in this paper, by using of frobenius theorem a relation between lie subalgebras of the lie algebra of a top space t and lie subgroups of t(as a lie group) is determined. as a result we can consider these spaces by their lie algebras. we show that a top space with the finite number of identity elements is a c^{∞} principal fiber bundle, by this method we can characterize top spaces.

Consider the Jacobian of a hyperelliptic genus two curve de ned over a nite eld. Under certain restrictions on the endomorphism ring of the Jacobian, we give an explicit description of all non-degenerate, bilinear, anti-symmetric and Galois-invariant pairings on the Jacobian. From this description it follows that no such pairing can be computed more e ciently than the Weil pairing. To establish...