The article introduces the concept of α–field as a generalization of field, σ–field, and δ–field, and explores its properties. It also discusses the relationships between σ–field and σ–field, showing that every σ–field is a β–field. The concept of β–field is introduced as a generalization of σ–field, β–σ–field, and ring, with important results obtained. Additionally, the concept of restriction of β–field is studied, proving that if ℘ is a β–field of a set ℵ and K is a non-empty subset of ℵ, then ℘|K is a β–field of set K.