New York Journal of Mathematics
Volume 20 (2014) 1063-1076


Venus Amjad, Kostaq Hila, and Faisal Yousafzai

Generalized hyperideals in locally associative left almost semihypergroups

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Published: November 26, 2014
Keywords: LA-semihypergroups, locally associative LA-semihypergroups, pure left identity and (m,n)-hyperideals
Subject: 20M10, 20N99

In this paper, we introduce the concept of a locally associative LA-semihypergroup by generalizing the idea of a locally associative LA-semigroup given in Mushtaq-Yusuf, 1979, and study an (m,n)-regular class of a locally associative LA-semihypergroup. We give some examples to connect an LA-semihypergroup with commutative hypergroups and commutative semihypergroups. We also characterize a locally associative LA-semihypergroup H in terms of (m,n)-hyperideals and prove that if R(L) is a 0-minimal right (left) hyperideal of H, then either Rm∘ Ln={0} or Rm∘ Ln is a 0-minimal (m,n)-hyperideal of H for m,n≧ 2.


The third author is highly thankful to CAS-TWAS President's Fellowship.

Author information

Venus Amjad:
Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan

Kostaq Hila:
Department of Mathematics & Computer Science, University of Gjirokastra, Gjirokastra, Albania

Faisal Yousafzai:
School of Mathematical Sciences, University of Science and Technology of China, Hefei, China