In algebra, the term Hermite ring (after Charles Hermite) has been applied to three different objects. According to Kaplansky (1949), a ring is right Hermite if, for every two elements a and b of the ring, there is an element d of the ring and an invertible 2×2 matrix M over the ring such that (a b)M = (d 0), and the term left Hermite is defined similarly.
In algebra, the term Hermite ring (after Charles Hermite) has been applied to three different objects. According to Kaplansky (1949), a ring is right Hermite if, for every two elements a and b of the ring, there is an element d of the ring and an invertible 2×2 matrix M over the ring such that (a b)M = (d 0), and the term left Hermite is defined similarly.
Source: Wikipedia "Hermite ring" · CC BY-SA 4.0
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