Boolean zero square (BZS)‎ semigroups

الملخص EN

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 ?∈?, we have ?2=? or ?2=0.

We obtain some properties that describe the behaviour of the Green’s equivalence relations ℛ, ℒ, ℋ and ?.

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.-