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The aim of this paper is to investigate homomorphisms which preserve square-free languages or primitive languages. A characterization of square-free-preserving homomorphisms is presented. We show that every square-free-preserving homomorphism is primitive-preserving. Strongly cube-free-preserving homomorphisms axe also studied

In this article, we focus on the properties of word-paired insertions of languages. We show that the word-paired insertions of discrete dense languages, the set of all d-primitive words, and the set of all primitive words are disjunctive (hence, dense and not regular). The equalities and the intersection-properties concerning word-paired insertions of languages are studied too

Many systems involve substitutions between some sets of elements. The 0L system is a known technique which can help us to investigate properties of substitutions systematically. The aim of this paper is to establish some properties of the P0L schemes which preserve some types of properties of languages. Characterizations of pure-language-preserving, dense-preserving and palindrome-preserving P0L schemes are proposed. s-Injective, primitivity preserving, d-primitivity preserving, prefix code preserving and maximal prefix code preserving substitutions are also studied. Properties of dense-generating 0L schemes are also investigated

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