As an application of the theory Lawson homology and morphic cohomology, Walker proved that Abel-Jacobi map factors through another regular homomorphism. In this note, we give a direct proof theorem.

The word u = abaaba satisfies f(u) = u where f maps b to aba and cancels a. Such words, which are fixed points of a nontrivial morphism, are called morphically imprimitive. On the other hand, the word u′ = abba can be easily verified to be morphically primitive, which means that the only morphism satisfying f(u′) = u′ defined on {a, b}∗ is the identity. Fixed points of word morphisms and morphi...

Episturmian morphisms constitute a powerful tool to study episturmian words. Indeed, any episturmian word can be infinitely decomposed over the set of pure episturmian morphisms. Thus, an episturmian word can be defined by one of its morphic decompositions or, equivalently, by a certain directive word. Here we characterize pairs of words directing a common episturmian word. As a consequence, we...

We study the logarithmic frequency of letters and words in morphic sequences and show that this frequency must always exist, answering a question of Allouche and Shallit.

We show that a ring $R$ has stable range one if and only every left unit lifts modulo principal ideal. also quasi-morphic it is uniquely generated. Thus we answer in the affirmative two questions raised by W. K. Nicholson.