Open AccessCorrections and Extensions in Left and Right Almost Semigroups
Author(s) -
Noor Azlinda Ahmad,
Syed Aleem Shah,
Wali Khan Mashwani,
Nasim Ullah
Publication year - 2021
Publication title -
the punjab university journal of mathematics
Language(s) - English
Resource type - Journals
ISSN - 1016-2526
DOI - 10.52280/pujm.2021.530703
Subject(s) - semigroup , cancellative semigroup , mathematics , bicyclic semigroup , commutative property , pure mathematics , zero (linguistics) , philosophy , linguistics
In this paper we elaborated the concept that on what conditions left almost semigroup (LA-Semigroup), right almost semigroup(RA-Semigroup) and a groupoid become commutative and further extended these results on medial, LA-Group and RA-Group. We provedthat the relation of LA-Semigroup with left double displacement semigroup (LDD-semigroup), RA-Semigroup with left double displacementsemigroup (RDD-semigroup) is only commutative property. We highlighted the errors in the recently developed results on LA-Semigroup andsemigroup [17, 1, 18] and proved that example discussed in [18] is semigroup with left identity but not paramedial. We extended results on locallyassociative LA-Semigroup explained in [20, 21] towards LA-Semigroupand RA-Semigroup with left zero and right zero respectively. We alsodiscussed results on n-dimensional LA-Semigroup, n-dimensional RASemigroup, non commutative finite medials with three or more than threeleft or right identities and finite as well as infinite commutative idempotentmedials not studied in literature.