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Ideals and Factor Rings

In: Ring Theory

Author

Listed:
  • Dinesh Khattar

    (University of Delhi, Department of Mathematics)

  • Neha Agrawal

    (University of Delhi, Department of Mathematics)

Abstract

Let us approach ideals in rings by way of a comparison with group theory. Group theory required us to refine our study of subgroups by examining the special case of normal subgroups. There is a neat structural parallel to be drawn here the notion of an ideal in a ring is analogous to the concept of a normal subgroup in groups. The similarities do not end here! Just as normal subgroups led us to the creation of quotient groups, in a similar way ideals do the job when we define quotient rings/factor rings.

Suggested Citation

  • Dinesh Khattar & Neha Agrawal, 2023. "Ideals and Factor Rings," Springer Books, in: Ring Theory, chapter 0, pages 79-136, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-29440-2_3
    DOI: 10.1007/978-3-031-29440-2_3
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