Unit 1
Maximal Ideals, the Field of Quotients of an Integral Domain, Euclidean Rings, Principal Ideal, Unit Element, Greatest Common Divisor, Prime Elements, Unique Factorization Theorem. (Sec. 3.5 to 3.7)
| Course Name | Advanced Algebra |
| Course Code | 26MAT332 |
| Program | 5 Year Integrated M.Sc in Data Science |
| Credits | 3 |
| Campus | Coimbatore |
Maximal Ideals, the Field of Quotients of an Integral Domain, Euclidean Rings, Principal Ideal, Unit Element, Greatest Common Divisor, Prime Elements, Unique Factorization Theorem. (Sec. 3.5 to 3.7)
The ring of Gaussian integers, Fermats Theorem, Polynomial Rings F[x], Degree of a Polynomial, The Division Algorithm, Principal Ideal Ring, Irreducible Polynomial, principal ideal ring. (Sec. 3.8 to 3.9)
Sub Fields, Field Extensions, Finite Extensions, Algebraic Extensions and Their Properties. The Transcendence of e. (Sec. 5.1 to 5.2)
Roots of Polynomials, Remainder Theorem, Splitting Field and its Uniqueness, The concept of constructible numbers and its Applications, Distinct and Multiple Roots, Simple Extension of a Field. (Sec. 5.3, 5.4, 5.5).
Text Book:
References:
This course gives a knowledge on advanced algebraic structures such a polynomial ring, Euclidean ring, PID, UFD and Extension Fields, etc. Students will study gcd, irreducible polynomials, and their splitting Field.
Course Outcomes: After successful completion of the course, students will be able to
| CO1 | To find field of quotient of integral domain and GCD of elements over Euclidean Ring. |
| CO2 | To study polynomial ring, Euclidean ring and PID. Also, to identify irreducible polynomials over various rings. |
| CO3 | To study the Field extension and algebraic extensions of a Filed. |
| CO4 | To identify roots and the splitting Field of a polynomial over a Field. |
Affinity Map:
| PO1 | PO2 | PO3 | PO4 | PO5 | PO6 | PO7 | PO8 | PO9 | PO10 | PO11 | PO12 | |
| CO1 | 1 | 3 | 2 | 3 | 1 | 2 | 1 | |||||
| CO2 | 1 | 3 | 2 | 3 | 1 | 2 | 1 | |||||
| CO3 | 1 | 3 | 2 | 3 | 1 | 2 | 1 | |||||
| CO4 | 1 | 3 | 2 | 3 | 1 | 2 | 1 | |||||
| CO5 | 1 | 3 | 2 | 3 | 1 | 2 | 1 |
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