Arya Bhatta Journal of Mathematics and Informatics
  • Year: 2023
  • Volume: 15
  • Issue: 1

A Note on Kernels of Group and Ring Homomorphisms

Department of Mathematics, Sardar Patel University of Police, Security and Criminal Justice, Opp. Vigyan Nagar-342037, Jodhpur, India

*E-mail: skpandey12@gmail.com

Online Published on 08 June, 2023.

Abstract

Among various other results we exhibit that each group is a kernel of a group homomorphism and each additive group as well as each ring can be seen as a kernel of a ring homomorphism. In addition we discuss the algebraic implications of the idea presented in this paper.

Keywords

Group, Ring, Ideal, Quotient group, Quotient ring