Pure projective, pure injective and -injective modules over trivial ring extensions Page 1
International Journal of Algebra and Computation Vol. 33, No. 4 (2023) 699–716 c© World …

We say that a ring K is (right) split by a subring A provided that A is an (right) A-module direct
summand of K. Then K is said to be a split extension of A. By a theorem of Azumaya [lJ, a …

A ring R is called a right WPF-ring (weak PF-ring) if R is a semiperfect right simple-injective
ring with essential right socle. The class of right WPF-rings is broader than that of right PF …

PM Cohn [3] has introduced the notion of purity for R-modules. With respect to purity, flat,
absolutely pure and regular modules are studied. In this paper we introduce and study the …

Let R be a ring and n be a non-negative integer. In this paper, we introduce and study the
notions of Gorenstein n-weak injective and Gorenstein n-weak flat modules by using the …

We introduce the notion of almost pseudo-injective modules (AP-injective modules), which
generalizes the idea of pseudo-injective and almost injective modules. In support, we …

Let R be a ring and I an ideal of R. We define and study I-pure submodules, I-FP-injective
modules, I-flat modules, I-coherent rings and I-semihereditary rings. Using the concepts of I …

In this paper, we study Ding injective modules over Frobenius extensions. Let R⊂ A be a
separable Frobenius extension of rings and M any left A-module, it is proved that M is a Ding …

ABSTRACT A module M is called strongly FP-injective if Ext i (P, M)= 0 for any finitely
presented module P and all i≥ 1.(Pre) envelopes and (pre) covers by strongly FP-injective …