Some remarks on the \(\theta\)-valent Chrysippian rings (Q2737550)

The concept of \(\theta\)-valued Chrysippian ring (CHR) was introduced by \textit{F. Ayissi Eteme} [Bases d'une mathématique \(\theta\)-valente chrysippienne, Thèse d'état, Lyon (1982); Rev. Roum. Math. Pures Appl. 37, 103-114 (1992; Zbl 0768.03036)]. NEWLINENEWLINENEWLINEA CHR resembles a \(\theta\)-valued Lukasiewicz-Moisil algebra (LMA) [cf. \textit{V. Boicescu, A. Filipoiu, G. Georgescu} and \textit{S. Rudeanu}, Lukasiewicz-Moisil algebras, Amsterdam: North-Holland (1991; Zbl 0726.06007)], except that the bounded distributive lattice is replaced by a Boolean ring and the Boolean endomorphisms are not required to satisfy \(I\leq J\rightarrow \varphi_I\leq\varphi_J\). The remarks in this paper confine to the case \(\theta=N\) and concern \(N\)-ultrafilters in CHRS. No proofs are given except for two counterexamples, one of them pointing out a mistake in the works of Ayissi Eteme quoted above.NEWLINENEWLINEFor the entire collection see [Zbl 0938.00016].