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Dejun Wu

Publications and source records attributed to Dejun Wu.

10 recordsLinked to original sources
arXiv2026

Heaps of modules: homological aspects

The definitions of projective objects and Gorenstein projective objects in the category of heaps of $T$-modules are posed, where $T$ is a truss. It is shown that a heap of $T$-modules $P$ is projective if and only if $\mathcal{G}_{e_p}(P)$ is a projective $R(T)$-module for all $e_p\in P$ and a heap of $T$-modules $M$ is BP Gorenstein projective if and only if $\mathcal{G}_{e_m}(M)$ is a Gorenstein projective $R(T)$-module for all $e_m\in M$. Moreover, we give a functorial description of the BP Gorenstein projective dimension. Finally, it is also proven that a unital truss $T$ is a Gorenstein truss if and only if $R(T)$ is an Iwanaga-Gorenstein ring.

math.RT↗
arXiv2024

Injectivity of modules over trusses

As the dual notion of projective modules over trusses, injective modules over trusses are introduced. The Schanuel Lemmas on projective and injective modules over trusses are exhibited in this paper.

math.RT↗
arXiv2024

Wakamatsu tilting subcategories and weak support tau-tilting subcategories in recollements

In this article, we prove that if (A, B, C) is a recollement of abelian categories, then Wakamatsu tilting (resp. weak support tau-tilting) subcategories in A and C can induce Wakamatsu tilting (resp. weak support tau-tilting) subcategories in B, and the converses hold under natural assumptions. As an application, we mainly consider the relationship of tau-cotorsion torsion triples in (A, B, C).

math.RT↗
arXiv2023

Cotorsion pairs in comma categories

Let A and B be abelian categories with enough projective and injective objects, and T : A-B a left exact additive functor. Then one has a comma category (B*T). It is shown that If T : A-B is X-exact, then (*X, X) is a (hereditary) cotorsion pair in A and (*Y, Y)) is a (hereditary) cotorsion pair in B if and only if ((*X, Y ), ) is a (hereditary) cotorsion pair in (B*T) and X and Y are closed under extensions. Furthermore, we characterize when special preenveloping classes in abelian categories A and B can induce special preenveloping classes in (B*T).

math.CT↗
arXiv2019

A refinement of Gorenstein flat dimension via the flat--cotorsion theory

We introduce a refinement of the Gorenstein flat dimension for complexes over an associative ring--the Gorenstein flat-cotorsion dimension--and prove that it, unlike the Gorenstein flat dimension, behaves as one expects of a homological dimension without extra assumptions on the ring. Crucially, we show that it coincides with the Gorenstein flat dimension for complexes where the latter is finite, and for complexes over right coherent rings--the setting where the Gorenstein flat dimension is known to behave as expected.

math.RA↗
arXiv2010

When an $\mathscr{S}$-closed submodule is a direct summand

It is well known that a direct sum of CLS-modules is not, in general, a CLS-module. It is proved that if $M=M_1\oplus M_2$, where $M_1$ and $M_2$ are CLS-modules such that $M_1$ and $M_2$ are relatively ojective (or $M_1$ is $M_2$-ejective), then $M$ is a CLS-module and some known results are generalized. Tercan [8] proved that if a module $M=M_{1}\oplus M_{2}$ where $M_{1}$ and $M_{2}$ are CS-modules such that $M_{1}$ is $M_{2}$-injective, then $M$ is a CS-module if and only if $Z_{2}(M)$ is a CS-module. Here we will show that Tercan's claim is not true.

math.RA↗
arXiv2010

On a question of Mohamed and Müller

A module $M$ is called H-supplemented if for every submodule $A$ of $M$ there is a direct summand $A'$ of $M$ such that $A+X=M$ holds if and only if $A'+X=M$ for any submodule $X$ of $M$. (Equivalently, for each $X\leq M$, there exists a direct summand $D$ of $M$ such that $(X+D)/D\ll M/D$ and $(X+D)/X\ll M/X$.) Direct summands and sums of H-supplemented modules are studied and a question posed by Mohamed and Müller in 1990 is answered in the negative.

math.RA↗