A Textbook of Algebraic Number Theory

Sudesh Kaur Khanduja is Emeritus Professor at the Department of Mathematics, Panjab University, India, and INSA Senior Scientist at the Indian Institute of Science Education and Research (IISER) Mohali, India. A PhD and master’s degree from Panjab University, India, her primary research interests are in algebraic number theory and valuation theory. With over 40 years of teaching experience at Panjab University and IISER Mohali, she has guided 12 PhD students and published over 85 research papers in reputed international journals. A fellow of The World Academy Sciences, the Indian Academy of Sciences, the National Academy of Sciences, and the Indian National Science Academy (INSA), Prof. Khanduja was awarded the Professor V.V. Narlikar Memorial Lecture Award of INSA in 2015. She also has participated in various programs promoting the cause of mathematics at Panjab University. She has visited and delivered lectures at various universities includingOhio State University, Columbus; University of Missouri, Columbia; University of Michigan, Ann Arbor; University of Saskatchewan, Canada; Nihon University, Japan; State University of Campinas, Brazil, and University of Konstanz, Germany.

1. Algebraic Integers, Norm and Trace.-2. Integral Basis and Discriminant.-3. Properties of the Ring of Algebraic Integers.- 4. Splitting of Rational Primes and Dedekind’s Theorem.-5. Dirichlet’s Unit Theorem.- 6. Prime Ideal Decomposition in Relative Extensions.- 7. Relative Discriminant and Dedekind’s Theorem on Ramified.- 8. Ideal Class Group.-9. Dirichlet’s Class Number Formula and its Applications.- 10. Simplified Class Number Formula for Cyclotomic, Quadratic Fields.