1968/04/01 by P. M. Cohn · 3 citations
Mathematics · #Rings, Modules, and Algebras #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models #Generalization #Ideal (ethics) #Mathematics #Pure mathematics #Algebra over a field #Philosophy
paper · doi:10.1017/s0305004100042791
openalex publication_date 1968/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
The importance of principal ideal domains (PIDs), both in algebra itself and elsewhere in mathematics is undisputed. By contrast, Bezout rings, ‡ although they represent a natural generalization of PIDs, play a much smaller role and are far less well known. It is true that many of the properties of PIDs are shared by Bezout rings, but the practical value of this observation is questioned by many on the grounds that most of the Bezout rings occuring naturally are in fact PIDs. However, there are several fairly natural methods of constructing Bezout rings from other rings, leading to wide classes of Bezout rings which are not PIDs, and it is the object of this paper to discuss some of these methods.