A note on the Artin map. II (Q921051)

The author continues the study of his ``generalized Artin map'' defined in part I (cf. the preceding review). He shows that this map is separable if the center of the corresponding Galois group is trivial; in this context a monoid homomorphism f: \(F\to M\), where F is a free commutative monoid with a set of free generators \(\{\) \(p\}\), is called separable if the following condition holds: \(a\in Ker(f)\) if and only if \(f(p)=1\) for all p/a. This result allows him to obtain information about the kernel of the generalized Artin map.