Excellence in Research and Innovation for Humanity

Jianmin Xing

Publications

5

Publications

5
16764
n− Strongly Gorenstein Projective, Injective and Flat Modules
Abstract:

Let R be a ring and n a fixed positive integer, we investigate the properties of n-strongly Gorenstein projective, injective and flat modules. Using the homological theory , we prove that the tensor product of an n-strongly Gorenstein projective (flat) right R -module and projective (flat) left R-module is also n-strongly Gorenstein projective (flat). Let R be a coherent ring ,we prove that the character module of an n -strongly Gorenstein flat left R -module is an n-strongly Gorenstein injective right R -module . At last, let R be a commutative ring and S a multiplicatively closed set of R , we establish the relation between n -strongly Gorenstein projective (injective , flat ) R -modules and n-strongly Gorenstein projective (injective , flat ) S−1R-modules. All conclusions in this paper is helpful for the research of Gorenstein dimensions in future.

Keywords:
Commutative ring, n-strongly Gorenstein projective, n-Strongly Gorenstein injective, n-strongly Gorenstein flat, S-ring.
4
16765
Strongly ω-Gorenstein Modules
Abstract:

We introduce the notion of strongly ω -Gorenstein modules, where ω is a faithfully balanced self-orthogonal module. This gives a common generalization of both Gorenstein projective (injective) modules and ω-Gorenstein modules. We investigate some characterizations of strongly ω -Gorenstein modules. Consequently, some properties under change of rings are obtained.

Keywords:
Faithfully balanced self-orthogonal module, ω-Gorenstein module, strongly ω-Gorenstein module, finite generated.
3
5990
Generalized Module Homomorphisms of Triangular Matrix Rings of Order Three
Authors:
Abstract:

Let T,U and V be rings with identity and M be a unitary (T,U)-bimodule, N be a unitary (U, V )- bimodule, D be a unitary (T, V )-bimodule . We characterize homomorphisms and isomorphisms of the generalized matrix ring Γ =  T M D 0 U N 0 0 V .

Keywords:
Generalized module homomorphism, ring homomorphism, isomorphisms, triangular matrix rings.
2
9997593
Gorenstein Projective, Injective and Flat Modules Relative to Semidualizing Modules
Abstract:

In this paper we study some properties of GC-projective, injective and flat modules, where C is a semidualizing module and we discuss some connections between GC-projective, injective and flat modules , and we consider these properties under change of rings such that completions of rings, Morita equivalences and the localizations.

Keywords:
Semidualizing module, C-projective(injective,flat), GC-projective (injective,flat), Commutative ring; Localizations .
1
9997594
Relative Injective Modules and Relative Flat Modules
Abstract:

Let R be a ring, n a fixed nonnegative integer. The concepts of (n, 0)-FI-injective and (n, 0)-FI-flat modules, and then give some characterizations of these modules over left n-coherent rings are introduced . In addition, we investigate the left and right n-FI-resolutions of R-modules by left (right) derived functors Extn(−,−) (Torn(−,−) ) over a left n-coherent ring, where n-FI stands for the categories of all (n, 0)- injective left R-modules. These modules together with the left or right derived functors are used to study the (n, 0)-injective dimensions of modules and rings.

Keywords:
(n, 0)-injective module, (n, 0)-injective dimension, (n, 0)-FI-injective(flat) module, (Pre)cover, (Pre)envelope.