PURE PROJECTIVITY AND PURE INJECTIVITY OVER FORMAL TRIANGULAR MATRIX
RINGS Page 1 Journal of Algebra and Its Applications Vol. 11, No. 6 (2012) 1250107 (13 …

Abstract Let Λ _ (0, 0)=\left (A\;\;\;\;\;\;\; _A N_B _B M_A\;\;\;\; B\cr\right) Λ (0 0)=(AANBBMAB)
be a Morita ring, where the bimodule homomorphisms ϕ and ψ are zero. We study the finite …

Recently, Xiang and Ouyang defined a (commutative unital) ring R to be Nil*-coherent if
each finitely generated ideal of R that is contained in Nil (R) is a finitely presented R-module …

Let R be a ring and Nil∗(R) be the prime radical of R. In this paper, we say that a ring R is
left Nil∗-coherent if Nil∗(R) is coherent as a left R-module. The concept is introduced as the …

Let be a ring graded by an arbitrary grading abelian group Γ. We say that R is a uniformly
graded-coherent ring if there is a map ϕ: ℕ→ ℕ such that for every n∈ ℕ, and any nonzero …

Let D be a domain with its quotient field K. Let K [θ]= K [x]/(xn) where x is an indeterminate
and θ= x+(xn). Denote by R n= D+ θ K [θ], which is a subring of K [θ]. This paper studies …

A right ideal I of a ring R is small in case for every proper right ideal K of R, K+ I ${\neq} $= R.
A right R-module M is called PS-injective if every R-homomorphism f: aR ${\rightarrow} $ M …

关于w-IFP-平坦模与w-IFP-内射模 Page 1 山东大学学报(理学版)2024年2月第59卷第2期 E-mail:xblxb@sdu.edu.cn
Journal of Shandong University(Natural Science)ꎬ Vol.59ꎬ No.2ꎬ 2024 http:/ / lxbwk.njournal.sdu.edu.cn …

This paper unifies several generalizations of coherent rings in one notion. Namely, we
introduce nX-coherent rings, where X is a class of modules and n is a positive integer, as …

Let be a ring, a class of left-modules, the class of submodules of, and the class of quotient-
modules of. It is shown that is precovering (preenveloping) if and only if every injective …