Let $ R $ be a ring, $ E= E (R_R) $ its injective envelope, $ S=\operatorname {End}(E_R) $
and $ J $ the Jacobson radical of $ S $. It is shown that if every finitely generated submodule …

Cukerman [2], Shanny [5], and Ware [7] have shown that a ring R is Artin semisimple if and
only if R has a nonfinitely generated free module with regular endomorphism ring. This …

Over a ring A let PA be a finitely generated projective right A-module with A-endomorphism
ring B. Anderson has called PA an injector, perfect injector, projector, perfect projector, if the …

Let R be a commutative ring, and let L and L′ be R-modules. We investigate finiteness
conditions (eg, noetherian, artinian, mini-max, Matlis reflexive) of the modules Ext R i (L, L′) …

All rings in this paper are associative with identity and all modules right unital. For any ring
R, let Rn= R x... x R and nR={bi, all b 6 Rn). Recall that b E Rn is said to be a una'moduhr …

Projective modules over the endomorphism ring of a biuniform module - ScienceDirect Skip
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Let RP be a projective R-module which is not finitely generated. Let E= End R (P). This
paper examines the structure of P as an E-module and relations between right ideals of R …

We prove here, among other results, that if R is a commutative noetherian ring and
projective R [x 1,…, xn]-modules of rank⩽ Krull dim R are extended, then finitely generated …

Let be a non-empty collection of right ideals of a ring R. A right R-module X is called-
injective provided each R-homomorphism ϕ: A→ X with A in can be lifted to an R …

In this paper, we prove that the injective cover of the R-module E (R/B)/R/B for a prime ideal
B of R is the direct sum of copies of E (R/B) for prime ideals D⊃ B, and if B is maximal, the …