Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Generalities on rings and modules -- 1. Principal ideal domains -- 2. Firs, semifirs and the weak algorithm -- 3. Factorization in semifirs -- 4. Rings with a distributive factor lattice -- 5. Modules over firs and semifirs -- 6. Centralizers and subalgebras -- 7. Skew fields of fractions.

Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends in a historical note.