Yuanlin Li

STRONGLY GORENSTEIN FLAT MODULES

In this paper, we investigate the strongly n-Gorenstein flat module. Namely, the class of the strongly n-Gorenstein flat module is projective resolving if and only if it is closed under the extension. Also, we generalize every flat module is strongly n-Gorenstein flat over n-perfect ring; every strongly n-Gorenstein flat module is Gorenstein flat over coherent and n-perfect ring

The normalizer of a metabelian group in its integral group ring

Abstract In this paper, we discuss two cases where all C -automorphisms are inner; therefore, the normalizer property holds for those cases. Our results generalize a result of Marciniak and Roggenkamp. As an application of our theorems, we prove that the normalizer property holds for the integral group ring of a split finite metabelian group with a dihedral Sylow 2-subgroup. Our proofs rely heavily on the method of Marciniak and Roggenkamp.

ON (m, n)-INJECTIVITY OF MODULES

Let R be a ring. For two fixed positive integers m and n, a right R-module M is called (m, n)-injective if every right R-homomorphism from an n-generated submodule of Rm to M extends to one from Rm to M. This definition unifies several definitions on generalizations of injectivity of modules. The aim of this paper is to investigate properties of the (m, n)-injective modules. Various results are developed, many extending known results.

The hypercentre and the

In this paper, we first show that the central height of the unit group of the integral group ring of a periodic group is at most 2. We t hen give a complete characterization of the n-centre of that unit group. The n-centre of the unit group is either the centre or the second centre (for n 2).

n

Let

-centre of the unit group of an integral group ring

G

MINIMAL ZERO-SUM SEQUENCES OF LENGTH FOUR OVER FINITE CYCLIC GROUPS II

be a finite cyclic group. Every sequence

ON THE DERIVED LENGTH OF THE GROUP OF UNITS OF A GROUP ALGEBRA

S

CLASS PRESERVING AUTOMORPHISMS OF BLACKBURN GROUPS

over

Reversible Group Rings Over Commutative Rings

G