The ring of Colombeau’s full generalized quaternions. (English) Zbl 1401.46030
The ring of Colombeau full generalized quaternions is introduced. The algebraic theory of Colombeau’s generalized numbers was proposed in [J. Aragona and S. O. Juriaans, Commun. Algebra 29, No. 5, 2201–2230 (2001; Zbl 1007.46037)]. Based on results of this seminal paper as well as on the more recent results of J. Aragona et al. [J. Algebra 384, 194–211 (2013; Zbl 1297.46031)], the algebraic properties of full generalized quaternions are studied, including the duo, exchange, normal, and the Bézout property. It is proved that the ring of Colombeau full generalized quaternions is Gelfand.
Reviewer: Denis Sidorov (Irkutsk)
MSC:
| 46F30 | Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) |
| 46F20 | Distributions and ultradistributions as boundary values of analytic functions |
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