Definition: (right Bezout) Finitely generated right ideals are cyclic

- A. A. Tuganbaev. Semidistributive modules and rings. (2012) @ Chapter 3

- stable under finite products
- stable under products
- forms an equational class
- passes to matrix rings

- passes to quotient rings (Counterexample: $R_{ 1 }$)
- passes to subrings (Counterexample: $R_{ 6 }$ is a subring of $R_{ 101 }$)

Rings

Legend

- = has the property
- = does not have the property
- = information not in database