Definition of "prime field"

Theorem 2. Each field contains a unique prime field.

1968, J. F. Schuh, Mathematical Tools for Modern Physics, Philips Technical Library, page 91

Applying Hensel's lemma to the discrete logarithm problem over prime fields reveals the rich geometric and algebraic structure underlying the problem.

2004, H. Gopalkrishna Gadiyar, K. M. Sangeeta Maini, R. Padma, Cryptography, Connections, Cocycles and Crystals: A p-adic Exploration of the Discrete Logarithm Problem, Anne Canteaut, Kapaleeswaran Viswanathan (editors), Progress in Cryptology - INDOCRYPT 2004: 5th International Conference, Proceedings, Springer, LNCS 3348, page 305

Since every field contains a prime field, by studying prime fields, and the way properties are passed over to extensions, Steinitz would attain a full picture of the structure of all possible fields.

2004, Leo Corry, Modern Algebra and the Rise of Mathematical Structures, 2nd edition, Springer (Birkhäuser), page 194