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INTRODUCTION TO ABSTRACT ALGEBRA (Vol. 2)
Pabitra K. Gouri & Bharati Saxena
First Published: 2025
ISBN: 978-81-94107-53-3
Pages: 432

CONTENTS

RING
- Unit 1: Basic Definition of Ring
- Unit 2: Elementary properties of ring
- Unit 3: Divisor of zero
- Unit 4: Units
- Unit 5: Integral multiple of an element

FIELD
- Unit 1: Integral Domain
- Unit 2: Division Ring (Skew Field)
- Unit 3: Field
- Unit 4: Subring
- Unit 5: Subfield

IDEALS AND QUOTIENT RING
- Unit 1: Ideals
- Unit 2: Principal ideal
- Unit 3: Prime ideal
- Unit 4: Maximal ideal
- Unit 5: Quotient Ring

FACTORIZATION DOMAIN
- Unit 1: Divisibility of an integral domain
- Unit 2: Unique Factorization Domain
- Unit 3: Principal Ideal Domain
- Unit 4: Euclidean Domain

HOMOMORPHISM OF RING
- Unit 1: Homomorphism of Ring
- Unit 2: Homomorphic image
- Unit 3: Kernel of ring homomorphism
- Unit 4: Isomorphism
- Unit 5: Ring embedding and field of quotient

POLYNOMIAL RING 
- Unit 1: Definition and elementary properties
- Unit 2: Divisibility of polynomial ring
- Unit 3: Irreducibility of polynomial ring

EXERCISES
BIBLIOGRAPHY
INDEX

ABOUT THE BOOK

- The book entitled 'Introduction to Abstract Algebra (Vol. 2)' has been written to serve as a textbook for the Undergraduate (Hons./Major) students of Mathematics of all Indian Universities according to the NEP syllabus as well as competitive examinations.
- This book is written in a lucid style and pointwise manner presenting the subject matter from basic elementary information to the most recent advances.
- One of the attractive features of this book is it's rich collection of problems and solutions that have been selected from different Universities’ question papers and model question papers that will greatly help the students.
- This book contains unit-end MCQs, and these are selected from different competitive examinations, namely CSIR UGC NET, GATE, NBHM, IIT JAM, and TIRFR.
- This book will help students not only to prepare for examinations but also enable them to develop analytical problem-solving skills.
- A bonus to the students: the authors are available for free interactive sessions at WhatsApp No. 8972644828 or pabitrakumargouri@gmail.com

ABOUT THE AUTHORS

Mr. Pabitra Kumar Gouri is an M.Sc. (First Class) in Applied Mathematics with Oceanology and Computer programming and has also obtained his professional qualification in B.Ed. Presently, he is the Head of Institution at Chhotakhelna S. S. Vidyamandir, Maligram, Paschim Medinipur, West Bengal, India. He was formerly Head of Institution at Saluka M. J. High School, Tamluk, Purba Medinipur, West Bengal, India. Formerly, he also served as an assistant teacher of Mathematics at Dubra Adarsha Vidyamandir (H.S), Jhargram, Paschim Medinipur, West Bengal, India. He is also the author of the books, 'Introduction to Abstract Algebra (Vol .1)' and 'Introduction to Linear Algebra' both published by Books & Allied (P) Ltd.

Dr. Bharti Saxena has an M.Sc. in Mathematics from B.U. and an M.Tech. from BUIT. She obtained her Ph.D. degree in Mathematics from Rabindranath Tagore University, Bhopal, Madhya Pradesh, India. Presently, she is an Associate Professor in Mathematics at Rabindranath Tagore University, Bhopal, Madhya Pradesh, India. She has published several research papers in National and International Journals. She has been honoured with the Srijan Award for Best Teacher in Discrete Structure from MPCST.