Properties of U-factorizations
u-factorizations, properties, zero-divisors, finite commulative rings, graphs
Let R be a commutative ring with identity. In this paper we examine a type of factorization called a U-factorization. We classify all possible rearrangements of U-factorizations and extend several results concerning finite factorization properties to U-factorizations. We explore the close relationship between a U-factorization in a ring R and a factorization in a related monoid, (R/∼,·), where ∼ is the associate relationship. We then examine U-factorizations in idealizations.
International Journal of Commutative Rings