A field K is called an n-dimensional local field if there is a sequence of fields kn, . . . , k0 satisfying the following conditions: k0 is a finite field, ki is a complete discrete valuation field with residue field ki−1 for i = 1, . . . , n, and kn = K . In [9] we defined a canonical homomorphism from the n th Milnor group Kn(K) (cf. [14]) of an n-dimensional local field K to the Galois group...

1.1. Throughout this paper, let S be a fixed, smooth (C ~) orientable closed surface of genus g > 2. Let S be equipped with a preferred complex structure; we denote the Riemann surface byX0, and the Teichmtiller space ofX o by T 0. There is a Fuchsian group Fg operating in the unit disk so that X o = U/F o. The universal Teichmiiller curve V o is a fibre space over Teichmtiller space, with Xt, ...

A mapping of k-bit strings into n-bit strings is called an (α, β)-map if k-bit strings which are more than αk apart are mapped to n-bit strings that are more than βn apart. This is a relaxation of the classical error-correcting codes problem (α = 0). The question is equivalent to existence of graph homomorphisms between certain graphs on the hypercube. Tools based on Schrijver’s θ-function are ...

In this paper, we describe linear maps between complex Banach algebras that preserve products equal to fixed elements. This generalizes some important special cases where the elements are zero or identity element. First show if such map preserves a finite-rank operator, then it must also product. several instances, is enough product preserving be scalar multiple of an algebra homomorphism. Seco...

In this paper, our aim was making a metric space on hoop algebras, because of that, we introduced the notion valuation maps from F-quasi-valuation map based hoops and related properties them are investigated. By using these notions, quasi-metric space. The continuity operations is studied with topology induced by quasi-valuation. Also, homomorphism investigated that under which condition an map...

We construct the homomorphism of presheaves ${\mathrm{K}}^\mathrm{MW}_* \to {\pi}^{*,*}$ over an arbitrary base scheme $S$, where $\mathrm{K}^\mathrm{MW}$ is (naive) Milnor-Witt K-theory presheave. Also we discuss some partly alternative proof (or proofs) isomorphism sheaves $\unKMW_n\simeq \underline{\pi}^{n,n}_s$, $n\in \mathbb Z$, a filed $k$ originally proved in \cite{M02} and \cite{M-A1Top}.

Given a transversely projective foliation F on a C∞ manifold M and a nonnegative integer k, a transversal differential operator DF (2k + 1) of order 2k + 1 from N⊗k to N⊗(−k−1) is constructed, where N denotes the normal bundle for the foliation. There is a natural homomorphism from the space of all infinitesimal deformations of the transversely projective foliation F to the first cohomology of ...

The algebra Sn of one-sided inverses of a polynomial algebra Pn in n variables is obtained from Pn by adding commuting, left (but not two-sided) inverses of the canonical generators of the algebra Pn. Ignoring non-Noetherian property, the algebra Sn belongs to a family of algebras like the nth Weyl algebra An and the polynomial algebra P2n. Explicit generators are found for the group Gn of auto...