Bezout Rings and Monoids

Multiplicative number theory and linear algebra lead to the investigation of Bezout rings (i.e., commutative rings whose finitely generated ideals are cyclic), as well as to the investigation of their semigroup (monoid) of principal ideals under multiplication. In this talk we discuss mainly the abstract characterization of such monoids. This question is a generalization of the classic result in valuation theory showing that every ordered abelian group is the value group of a suitable valued field.