E-games: a very short introduction

The Dirichlet's Unit Theorem describes the structure of the group of units as follows: let K be an algebraic number field with $r_1$ real and $2r_2$ complex embeddings and ring of integers $O_K$ . Then the group of units of $O_K$ is equal to the direct product of the finite cyclic group E(K) of roots of unity contained in K and a free abelian group of rank $r: = r_1+ r_2 - 1$. Dirichlet's E-symbol ("container" of the numbers of a special type) became the object of Nikolai Bugaev's mathematical dissertation.Bugaev and his followers of Moscow's Philosophical Mathematical School have attempted to develop a sort of E-games which we define today as noncooperative signaling games in post-Quantum perspective. Our very short introduction in E-games describes historical circumstances and the reasons for introduction of E-games in post-quantum game theory. Fundamental Riemann problem and ABC conjecture in Number theory are considered also as an examples of E-game, hence, game-theoretical approach in Number theory is firstly justified.