Open AccessBoolean Zero Square (BZS) Semigroups
Author(s) -
Gama Pinto
Publication year - 2021
Publication title -
maǧallaẗ ǧāmiʿaẗ al-sulṭān qābūs li-l-ʿulūm/sultan qaboos university journal for science
Language(s) - English
Resource type - Journals
eISSN - 2414-536X
pISSN - 2308-3921
DOI - 10.53539/squjs.vol26iss1pp31-39
Subject(s) - mathematics , semigroup , special classes of semigroups , square (algebra) , zero (linguistics) , pure mathematics , cancellative semigroup , bicyclic semigroup , inverse semigroup , discrete mathematics , inverse , linguistics , philosophy , geometry
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 or . We obtain some properties that describe the behaviour of the Green’s equivalence relations , , 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.