B.Sc Curriculum - Madras Christian College
B.Sc Curriculum - Madras Christian College
B.Sc Curriculum - Madras Christian College
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Algebraic Structures<br />
Part III (a) – Major Credits: 4<br />
Semester III - Paper V Hours / Cycle: 5<br />
UNIT I Hours: 15<br />
Group Theory: Groups – Subgroups – Counting Principle – Normal Subgroups<br />
Chapter 2: Sections 2.1 – 2.6<br />
UNIT II Hours: 15<br />
Homomorphisms – Automorphisms – Cayley’s theorem – Permutation groups.<br />
Chapter 2: Sections2.7 – 2.10(omit application 1 and 2)<br />
UNIT III Hours: 15<br />
Ring Theory: Definition and examples of Rings – Some special classes of rings –<br />
Homomorphisms.<br />
Chapter 3: Sections 3.1 – 3.3<br />
UNIT IV Hours: 15<br />
Ideals and Quotient rings: More ideals and Quotient ideals – field of quotients of an integral<br />
domain.<br />
Chapter 3: Sections 3.4 – 3.6<br />
UNIT V Hours: 15<br />
Euclidean rings: A particular Euclidean ring – Polynomial Rings – Polynomials over the<br />
rational field.<br />
Chapter 3: Sections 3.7 – 3.10<br />
Treatment and content as in<br />
Topics in Algebra, Second Edition,I.N. Herstein, Wiley Student edition, 2009.<br />
References<br />
1. Modern Algebra, M.L. Santiago, Tata McGraw-Hill Publishing Co. Ltd, 2001.
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