In papers written in the fifties, especially in the series Quantum Mechanics and Geometry , Mario Schönberg introduces and analyzes several algebraic structures obtained from simple geometric objects, such as vectors and points. With these geometric algebras, he then proceedes to investigate a new algebraic formalism for the physical world, in particular for quantum mechanics, based on a deeper mathematical understanding of space-time and its relations with other properties of matter. In this work, we single out a special anticommutative algebra and, as an application to physics, relate it to the algebra of operators for fermionic second quantization.