A note on CSP rings

A note on CSP graph parameters

Several graph parameters such as induced width, minimum maximum clique size of a chordal completion, k-tree number, bandwidth, front length or minimum pseudo-tree height are available in the CSP community to bound the complexity of specific CSP instances using dedicated algorithms. After an introduction to the main algorithms that can exploit these parameters, we try to exhaustively review exis...

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