Multidimensional extension of the Morse–Hedlund theorem

Multidimensional extension of the Morse-Hedlund theorem

A celebrated result of Morse and Hedlund, stated in 1938, asserts that a sequence x over a finite alphabet is ultimately periodic if and only if, for some n, the number of different factors of length n appearing in x is less than n+1. Attempts to extend this fundamental result, for example, to higher dimensions, have been considered during the last fifteen years. Let d ≥ 2. A legitimate extensi...

An extension of the Wedderburn-Artin Theorem

‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

The Extension Theorem

Given a compact convex polyhedron, can it tile space in a transitive (or in a regular) way? We discuss in the paper the so-called extension theorem giving conditions under which there is unique extension of a finite polyhedral complex, which consists of replicas of the given polyhedron, to a global isohedral tiling. The extension theorem gives a way to get all possible regular tilings with the ...

Extension of Krull's intersection theorem for fuzzy module

‎In this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules.  It shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. We investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. Finally we extend Krull's intersection theorem of fuzzy ideals by using concept $mu$-adic comp...