Multiplicative properties of integer valued polynomials over split-quaternions

Abstract

We study localization properties and the prime spectrum of the integer-valued polynomial ring $\mathrm{I}\mathrm{n}{\mathrm{t}}_{{\mathbb{P}}_{\mathbb{Q}}}({\mathbb{P}}_{\mathbb{Z}}),$ where ${\mathbb{P}}_{\mathbb{Z}}$ (respectively ${\mathbb{P}}_{\mathbb{Q}}$) is the algebra of split-quaternion over ℤ (respectively over $\mathbb{Q}$).

Keywords:

• Krull dimension
• prime ideal
• quaternion algebra

2010 Mathematics Subject Classification:

• Primary: 11R52
• 16H05
• 13F20

Acknowledgements

We would like to thank the referee for his/her useful suggestions.

Additional information

Funding

The second and third authors were partially supported by GNSAGA of Istituto Nazionale di Alta Matematica.