41. Fix a finite field GF ( q ), where q is a prime power. 42. In particular, this applies to finite field extensions of " K ". 43. And we consider this as defining an algebraic curve over the finite field with elements. 44. Both of these approaches may evaluate the elements of the finite field in any order. 45. Every finite field is a simple extension of the prime field of the same characteristic. 46. Dowling lattice of the multiplicative group of a finite field " F ". 47. This is because addition in any characteristic two finite field reduces to the XOR operation. 48. The non-zero elements of a finite field form a cyclic group under multiplication. 49. Every hyperfinite field is pseudo-finite and every pseudo-finite field is quasifinite. 50. The number of elements of a finite field is called its " order ".
