Classification of 8-dimensional rank two commutative semifields (Q1737108)

A semifield is a possibly non-associative algebra with a multiplicative identity and with no zero divisors. Its centre is the intersection of its nucleus and its commutative centre. The authors give a computational classification of the rank two commutative semifields which are 8-dimensional over their center which relies on previously found bounds and on the size of the centre as a function of dimension. These methods are then used to complete the classification of rank two commutative semifields which are 10-dimensional over the field of order 3. These results have implications for semifield flocks, ovoids of parabolic quadrics, and eggs.