Commutative Theorem for Rings

1. COMMUTATIVITY
THEOREMS FOR RINGS
D. RENUGA,
ASST. PROF. OF MATHEMATICS,
SAC WOMEN'S COLLEGE, CUMBUM,
THENI(DT),

2.  During the last 55 years there have been many results concerning
conditions that force a ring to be commutative. These results were simulated by
Jacobson’s famous result and were extensively developed by Herstein.
 The genesis of the theories of commutative rings and noncommutative rings
back to the early 19th century, while their maturity was achieved only in third
decade of the 20th century.

8. Ring theory may be used to understand the following :
• Physical laws such as those underlying special relativity
• Symmetry phenomena in molecular chemistry

21. CONCLUSION
we investigated about rings and commutative rings. And we collected the
definitions and examples related to this topic, “Commutativity theorems for rings”.
We examined about the commutativity theorems which are proved using of an
iteration technique and Jordan structure. We discussed about the theorems for
certain classes of ring such as Boolean ring. Moreover, commutativity theorems for
prime rings are also discussed. We examined one or two theorems also discussed. We
examined one or two theorems related to this topic. But there are lot of theorems for
ring which is a commutative, it can be proved using of an involution, constraints on
commutators, polynomial constraints apart from above we mentioned, and we hope
to study many of it in future.

22. THANK YOU