Abstract Group Generated by the Quaternion Units

Groups generated by two bicyclic units in integral group rings

Stable Rings Generated by Their Units

We introduce the class of rings satisfying (m,1)-stable range and investigate equivalent characterizations of such rings. These give generalizations of the corresponding results by Badawi (1994), Ehrlich (1976), and Fisher and Snider (1976). 2000 Mathematics Subject Classification. 19B10, 16E50. Let R be an associative ring with identity. A ring R is said to have stable range one provided that ...

A pr 2 00 9 Group Rings that are Additively Generated by Idempotents and Units

Let R be an Abelian exchange ring. We prove the following results: 1. RZ2 and RS3 are clean rings. 2. If G is a group of prime order p and p is in the Jacobson radical of R, then RG is clean. 3. If identity in R is a sum of two units and G is a locally finite group, then every element in RG is a sum of two units. 4. For any locally finite group G, RG has stable range one. All rings in this note...

Quaternion Higgs and the Electroweak Gauge Group

We show that, in quaternion quantum mechanics with a complex geometry, the minimal four Higgs of the unbroken electroweak theory naturally determine the quaternion invariance group which corresponds to the Glashow group. Consequently, we are able to identify the physical significance of the anomalous Higgs scalar solutions. We introduce and discuss the complex projection of the Lagrangian density.

The Group Generated by Unipotent Operators1

The group generated by unipotent n X n complex matrices is SL„(C), and every member of the latter is a product of three unipotent matrices. The group generated by unipotent operators on Hilbert space Jf is GL(Jf ), and every invertible operator is a product of six unipotent operators of order 2. An operator U on a Hilbert space is called unipotent [3, p. 100] if U = 1 + N, where N is nilpotent....