A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characte...

Gillespie posed two questions in [Front. Math. China 12 (2017) 97-115], one of which states that “for what rings R do we have K(AC)=K(R-Inj)?”. We give an answer to such a question. As applications, obtain new homological approach unifies some well-known conditions Krause’s recollement holds, and example show there exists Gorenstein injective module is not AC-injective. also improve Neeman’s an...

In (2003), we proved the injective homotopy exact sequence of modules by a method that does not refer to any elements of the sets in the argument, so that the duality applies automatically in the projective homotopy theory (of modules) without further derivation. We inherit this fashion in this paper during our process of expanding the homotopy exact sequence. We name the resulting doubly infin...

Let $T=\biggl(\begin{matrix} A&0\\U&B\end{matrix}\biggr)$ be a formal triangular matrix ring, where $A$ and $B$ are rings $U$ is $(B, A)$-bimodule. We first give some computing formulas of projective, injective, flat $FP$-injective dimensions special left $T$-modules. Then we establish (weak) global $T$. It proven that (1) If $U_{A}$ $_{B}U$ $lD(A)\neq lD(B)$, then $lD(T)={\rm m...

In this paper, we investigate the relative dominant dimension with respect to an injective module and characterize algebras finite dimension. As application, introduce almost n-precluster tilting establish a correspondence between modules n-minimal Auslander-Gorenstein algebras. Moreover, give description of Gorenstein projective over in terms corresponding modules.

We prove that if a positively-graded ring R is Gorenstein and the associated torsion functor has finite cohomological dimension, then the corresponding noncommutative projective scheme Tails(R) is a Gorenstein category in the sense of [10]. Moreover, under this condition, a (right) recollement relating Gorensteininjective sheaves in Tails(R) and (graded) Gorenstein-injective R-modules is given.

In this paper, we prove that the global Gorenstein projective dimension of a ring R is equal to the global Gorenstein injective dimension of R, and that the global Gorenstein flat dimension of R is smaller than the common value of the terms of this equality.

Let φφ be an Orlicz function that has a complementary function φφ∗ and let llφφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev’s Sum Inequality in llφφ⨂� FFXX, the Fremlin projective tensor product of llφφ with a Banach lattice X, and in llφφ⨂� iiXX, the Wittstock injective tensor product of llφφ with a Banach lattice X.

Given a complex projective algebraic variety, write H•(X,C) for its cohomology with complex coefficients and IH •(X,C) for its Intersection cohomology. We first show that under some fairly general conditions the canonical map H•(X,C) → IH •(X,C) is injective. Now let Gr := G((z))/G[[z]] be the loop Grassmannian for a complex semisimple group G, and let X be the closure of a G[[z]]-orbit in Gr. ...