We introduce a new class of semigroups, that we call BZS - Boolean Zero Square-semigroups. A semigroup S with a zero element, 0, is said to be a BZS semigroup if, for every 𝑥∈𝑆, we have 𝑥2=𝑥 or 𝑥2=0. We obtain some properties that describe the behaviour of the Green’s equivalence relations ℛ, ℒ, ℋ and 𝒟. Necessary and sufficient conditions for a BZS semigroup to be a band and an inverse semigroup are obtained. A characterisation of a special type of BZS completely 0-simple semigroup is presented.

We introduce a new class of semigroups, that we call BZS - Boolean Zero Square-semigroups. A semigroup S with a zero element, 0, is said to be a BZS semigroup if, for every 𝑥∈𝑆, we have 𝑥2=𝑥 or 𝑥2=0. We obtain some properties that describe the behaviour of the Green’s equivalence relations ℛ, ℒ, ℋ a...