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EDUCATION FACULTY / ELEMENTARY MATHEMATICS EDUCATION / IMZ3007 - ALGEBRA
GENERAL INFORMATION ABOUT THE COURSE
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Theoretical
Practical
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Course Objective
The purpose of this course is to examine algebraic structures such as groups, rings, and fields, and the relationships between them.
Brief Content of the Course
Binary operations, definition of a group and basic properties, subgroups, permutation groups, cyclic groups, symmetry group of a regular n-gon, cyclic permutations, odd and even permutations, homomorphisms, cosets and Lagrange's theorem, isomorphism theorems, action of a group on a set, rings, subrings and ideals, prime and maximal ideals, ring homomorphisms, arithmetic on rings, polynomial rings, fields; Burnside's theorem and its applications, p-groups and related theorems, simplicity of A_n for n > 4.
Prerequisites
Course Objectives
Course Objectives
1
1. Defines groups and subgroups.
2
2. Expresses and proves theorems related to Lagrange and Isomorphism.
3
3. Knows the definition of rings and subrings. Solves problems related to rings and subrings.
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Expertise /Field Courses