Characteristics of link primeness in terms of pseudo-characters

Pseudo-characters of Artin's braid groups and properties of links represented by braids are studied. The notion of kernel pseudo-character is introduced. It is proved that if a kernel pseudo-character $\phi$ and a braid $\beta$ satisfy $|\phi(\beta)|>C_\phi$, where $C_\phi$ is the defect of $\phi$, then $\beta$ represents a prime (i.e., noncomposite, nonsplit, and nontrivial) link. A method for obtaining nontrivial kernel pseudo-characters from an arbitrary nontrivial braid group pseudo-character is described. Bibl. – 17 titles.