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Yongduo Wang

Publications and source records attributed to Yongduo Wang.

9 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↗
arXiv2025

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↗
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↗
arXiv2011

A generalization of supplemented modules

Let $M$ be a left module over a ring $R$ and $I$ an ideal of $R$. $M$ is called an $I$-supplemented module (finitely $I$-supplemented module) if for every submodule (finitely generated submodule) $X$ of $M$, there is a submodule $Y$ of $M$ such that $X+Y=M$, $X\cap Y\subseteq IY$ and $X\cap Y$ is PSD in $Y$. This definition generalizes supplemented modules and $δ$-supplemented modules. We characterize $I$-semiregular, $I$-semiperfect and $I$-perfect rings which are defined by Yousif and Zhou [15] using $I$-supplemented modules. Some well known results are obtained as corollaries.

math.RA↗
arXiv2011

Characterizations of I-semiregular and I-semiperfect rings

Let $M$ be a left module over a ring $R$ and $I$ an ideal of $R$. We call $(P, f)$ a (locally)projective $I$-cover of $M$ if $f$ is an epimorphism from $P$ to $M$, $P$ is (locally)projective, $Kerf\subseteq IP$, and whenever $P=Kerf+X$, then there is a projective summand $Y$ of $P$ in $Kerf$ such that $P=Y\oplus X$. This definition generalizes (locally)projective covers. We characterize $I$-semiregular and $I$-semiperfect rings which are defined by Yousif and Zhou [19] using (locally)projective $I$-covers in section 2 and 3. $I$-semiregular and $I$-semiperfect rings are characterized by projectivity classes in section 4. Finally, the notion of $I$-supplemented modules are introduced and $I$-semiregular and $I$-semiperfect rings are characterized by $I$-supplemented modules. Some well known results are obtained as corollaries.

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↗