Event № 686
Advisor: Shai Haran
Abstract: We discuss the notion of a non-reduced arithmetic plane of the integers Z tensored with itself over F_1, the field with one element. It is a coproduct object in the category FR_c, which is a strictly larger category than the category of commutative rings (but there is an fully- faithfull embedding). We study its combinatorics, algebraic properties and show a connection with commutative rings.