A note on universally catenary rings

A Note on Rings of Finite Rank

The rank rk(R) of a ring R is the supremum of minimal cardinalities of generating sets of I as I ranges over ideals of R. Matson showed that every n ∈ Z+ occurs as the rank of some ring R. Motivated by the result of Cohen and Gilmer that a ring of finite rank has Krull dimension 0 or 1, we give four different constructions of rings of rank n (for all n ∈ Z+). Two constructions use one-dimension...

A Note on א0-injective Rings

A ring R is called right א0-injective if every right homomorphism from a countably generated right ideal of R to RR can be extended to a homomorphism from RR to RR. In this note, some characterizations of א0-injective rings are given. It is proved that if R is semiperfect, then R is right א0injective if and only if every homomorphism from a countably generated small right ideal of R to RR can b...

A Note on /-regularity in Rings

A Note on Moufang-lie Rings

A Note on Radicals of Seminear-rings

We generalize a few results of [2, 6, 8] for radical classes of rings for radical classes of seminear-rings by using the construction for radical classes of seminear-rings. AMS Mathematics Subject Classification (2000): 16Y60, 16W50