Multiplicative norms for metric rings

ADMITTING CENTER MAPS ON MULTIPLICATIVE METRIC SPACE

‎In this work‎, ‎we investigate admitting center map on multiplicative metric space‎ ‎and establish some fixed point theorems for such maps‎. ‎We modify the Banach contraction principle and‎ ‎the Caristi's fixed point theorem for M-contraction admitting center maps and we prove some‎ ‎useful theorems‎. ‎Our results on multiplicative metric space improve and modify‎ ‎s...

Sagbi Bases in Rings of Multiplicative Invariants

Let k be a field and G be a finite subgroup of GLn(Z). We show that the ring of multiplicative invariants k[x±1 1 , . . . , x ±1 n ] G has a finite SAGBI basis if and only if G is generated by reflections.

Metric engineering of supramolecular Borromean rings.

Two homologues of supramolecular Borromean rings were obtained based on the halogen-bonding-driven self-assembly of iodide ions with telechelic diiodoperfluoroalkanes.

On some subgroups of the multiplicative group of finite rings

Let S be a subset of Fq, the field of q elements and h ∈ Fq[x] a polynomial of degree d > 1 with no roots in S. Consider the group generated by the image of {x − s | s ∈ S} in the group of units of the ring Fq[x]/(h). In this paper we present a number of lower bounds for the size of this group. Our main motivation is an application to the recent polynomial time primality testing algorithm [AKS]...

Additive and Multiplicative Loops of Planar Ternary Rings