ON RINGS CONTAINING A P-INJECTIVE MAXIMAL LEFT IDEAL

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...

Lexicodes over Finite Principal Left Ideal Rings

Let R be a finite principal left ideal ring. Via a total ordering of the ring elements and an ordered basis a lexicographic ordering of the module R is produced. This is used to set up a greedy algorithm that selects vectors for which all linear combination with the previously selected vectors satisfy a pre-specified selection property and updates the to-be-constructed code to the linear hull o...

On semiperfect rings of injective dimension one

We give a characterization of right Noetherian semiprime semiperfect and semidistributive rings with inj. dimAAA 6 1.

On Maximal Ideal of Skew Polynomial Rings over a Dedekind Domain

Injective Modules and Fp-injective Modules over Valuation Rings

It is shown that each almost maximal valuation ring R, such that every indecomposable injective R-module is countably generated, satisfies the following condition (C): each fp-injective R-module is locally injective. The converse holds if R is a domain. Moreover, it is proved that a valuation ring R that satisfies this condition (C) is almost maximal. The converse holds if Spec(R) is countable....