Nisar Ahmad, Syed Aleem Shah, W. K. Mashwani, Nasim Ullah
{"title":"Corrections and Extensions in Left and Right Almost Semigroups","authors":"Nisar Ahmad, Syed Aleem Shah, W. K. Mashwani, Nasim Ullah","doi":"10.52280/pujm.2021.530703","DOIUrl":null,"url":null,"abstract":"In this paper we elaborated the concept that on what conditions left almost semigroup (LA-Semigroup), right almost semigroup\n(RA-Semigroup) and a groupoid become commutative and further extended these results on medial, LA-Group and RA-Group. We proved\nthat the relation of LA-Semigroup with left double displacement semigroup (LDD-semigroup), RA-Semigroup with left double displacement\nsemigroup (RDD-semigroup) is only commutative property. We highlighted the errors in the recently developed results on LA-Semigroup and\nsemigroup [17, 1, 18] and proved that example discussed in [18] is semigroup with left identity but not paramedial. We extended results on locally\nassociative LA-Semigroup explained in [20, 21] towards LA-Semigroup\nand RA-Semigroup with left zero and right zero respectively. We also\ndiscussed results on n-dimensional LA-Semigroup, n-dimensional RASemigroup, non commutative finite medials with three or more than three\nleft or right identities and finite as well as infinite commutative idempotent\nmedials not studied in literature.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"43 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Punjab University Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52280/pujm.2021.530703","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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 proved
that the relation of LA-Semigroup with left double displacement semigroup (LDD-semigroup), RA-Semigroup with left double displacement
semigroup (RDD-semigroup) is only commutative property. We highlighted the errors in the recently developed results on LA-Semigroup and
semigroup [17, 1, 18] and proved that example discussed in [18] is semigroup with left identity but not paramedial. We extended results on locally
associative LA-Semigroup explained in [20, 21] towards LA-Semigroup
and RA-Semigroup with left zero and right zero respectively. We also
discussed results on n-dimensional LA-Semigroup, n-dimensional RASemigroup, non commutative finite medials with three or more than three
left or right identities and finite as well as infinite commutative idempotent
medials not studied in literature.