A Classification of the Projective Lines over Small Rings II. Non-Commutative Case
Résumé
A list of different types of a projective line over non-commutative rings with unity of order up to thirty-one inclusive is given. Eight different types of such a line are found. With a single exception, the basic characteristics of the lines are identical to those of their commutative counterparts. The exceptional projective line is that defined over the non-commutative ring of order sixteen that features ten zero-divisors and it most pronouncedly differs from its commutative sibling in the number of shared points by the neighbourhoods of three pairwise distant points (three versus zero), that of ``Jacobson" points (zero versus five) and in the maximum number of mutually distant points (five versus three).
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