## ALGEBRAIC STRUCTURES IN TEACHER TRAINING PROGRAMS FOR BS, MS AND PHD DEGREES IN MATHEMATICS AT THE PEDAGOGICAL COLLEGE OF HUE UNIVERSITY

*Nguyen Xuan Tuyen*

`nxtuyenvn@yahoo.com`

Mathematics

**Pedagogical College of Hue University**

32 Le Loi street

VIETNAM

### Abstract

In the programs established for the degrees of Bachelor of Science (BS), Master of Science (MS) and Doctor of Philosophy (PhD) at the Pedagogical College of Hue University, four essential algebraic structures (group, ring, module, algebra) are grouped into two fundamental subjects: "groups & modules", and "modules & algebras". Next, there will be different applications and generalisations of these two subjects according to the aims for different degrees. For the training of high school teachers who already have a BS degree, these essential algebraic structures are constructed into three units: polynomial algebra, theory of numbers and, theory of Galois; for the training of the MS and PhD degrees, the algebraic structures are generalised onto the following units: foundation of algebra, theory of rings and modules, rings with finite conditions, theory of semirings and semimodules, commutative algebra, homological algebra, etc. In this paper, the programs for the following units are presented: Modules and algebras, Polynomial algebra, Foundation of algebra, Theory of semirings and semimodules.

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