In this paper, we introduce and study the notion of linkage modules by reflexive homomorphisms. This unifies generalizes several known concepts enables us to theory over Cohen–Macaulay rings rather than more restrictive Gorenstein rings. It is shown that results for are still true in general case module We also colinkage establish an adjoint equivalence between linked colinked modules.

In this work we consider morphisms that preserve well-known non-repeating properties: squarefreeness, cubefreeness, overlap-freeness and weak squarefreeness. Up to the present moment only the morphisms preserving three out of four non-repeating properties have been known. The problem of the existence of weakly squarefree morphisms was open. The essential result of this work is the positive solu...

Fixed points u = φ(u) of marked and primitive morphisms φ over arbitrary alphabet are considered. We show that if u is palindromic, i.e., its language contains infinitely many palindromes, then some power of φ has a conjugate in class P. This class was introduced by Hof, Knill and Simon (1995) in order to study palindromic morphic words. Our definitions of marked and well-marked morphisms are m...