The ring of Colombeau’s full generalized quaternions

ABSTRACT

In this paper, we introduce the ring of Colombeau full generalized quaternion, and we study its algebraic and topological properties. We prove that the ring of Colombeau full generalized quaternion is Gelfand, normal, duo and some related properties. Moreover, we study the essential ideals of this ring.

KEYWORDS:

• Generalized quaternion algebra
• noncommutative rings and ideals
• prime and maximal ideals

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 46F30
• Secondary: 46F20

Acknowledgments

The authors are grateful to UAMat/CCT/UFCG and CCEN/UFERSA where this work was realized. The second author thanks PNPD/CAPES for their support.

The ARGG author was partially supported by PNPD/CAPES.