Primitive group rings

Authors:
Edward Formanek and Robert L. Snider

Journal:
Proc. Amer. Math. Soc. **36** (1972), 357-360

MSC:
Primary 16A26; Secondary 20C05

MathSciNet review:
0308178

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Two theorems showing the existence of primitive group rings are proved.

Theorem 1. *Let G be a countable locally finite group and F a field of characteristic 0, or characteristic p if G has no elements of order p. Then the group ring* *is primitive if and only if G has no finite normal subgroups.*

Theorem 2. *Let G be any group, and F a field. Then there is a group H containing G such that* *is a primitive ring*.

**[1]**Ian G. Connell,*On the group ring*, Canad. J. Math.**15**(1963), 650–685. MR**0153705****[2]**Irving Kaplansky,*“Problems in the theory of rings” revisited*, Amer. Math. Monthly**77**(1970), 445–454. MR**0258865****[3]**Donald S. Passman,*Infinite group rings*, Marcel Dekker, Inc., New York, 1971. Pure and Applied Mathematics, 6. MR**0314951****[4]**Alan Rosenberg,*On the primitivity of the group algebra*, Canad. J. Math.**23**(1971), 536–540. MR**0286836**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
16A26,
20C05

Retrieve articles in all journals with MSC: 16A26, 20C05

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1972-0308178-8

Keywords:
Group ring,
primitive ring,
prime ring

Article copyright:
© Copyright 1972
American Mathematical Society