AUTHOR=Rao Yongsheng , Xu Peng , Shao Zehui , Kosari Saeed , Omidi Saber 

TITLE=Some Properties of Relative Bi-(Int-)Γ-Hyperideals in Ordered Γ-Semihypergroups

JOURNAL=Frontiers in Physics

VOLUME=8

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.555573

DOI=10.3389/fphy.2020.555573

ISSN=2296-424X

ABSTRACT=<p>In this article, we study the concept of relative bi-<inline-formula id="inf1"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>Γ</mml:mtext></mml:math></inline-formula>-hyperideals (<inline-formula id="inf2"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">J</mml:mi></mml:math></inline-formula>-bi-<inline-formula id="inf3"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>Γ</mml:mtext></mml:math></inline-formula>-hyperideals) in ordered <inline-formula id="inf4"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>Γ</mml:mtext></mml:math></inline-formula>-semihypergroups and present some related examples of this concept. Especially, characterization of <inline-formula id="inf5"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">J</mml:mi></mml:math></inline-formula>-simple ordered <inline-formula id="inf6"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>Γ</mml:mtext></mml:math></inline-formula>-semihypergroups in terms of <inline-formula id="inf7"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">J</mml:mi></mml:math></inline-formula>-bi-<inline-formula id="inf8"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>Γ</mml:mtext></mml:math></inline-formula>-hyperideals is given. Furthermore, we define the notion of <inline-formula id="inf9"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">J</mml:mi></mml:math></inline-formula>-(bi-)int-<inline-formula id="inf10"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>Γ</mml:mtext></mml:math></inline-formula>-hyperideals in ordered <inline-formula id="inf11"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>Γ</mml:mtext></mml:math></inline-formula>-semihypergroups and investigate its related properties. We show that <inline-formula id="inf12"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">J</mml:mi></mml:math></inline-formula>-int-<inline-formula id="inf13"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>Γ</mml:mtext></mml:math></inline-formula>-hyperideals and <inline-formula id="inf14"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">J</mml:mi></mml:math></inline-formula>-<inline-formula id="inf15"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>Γ</mml:mtext></mml:math></inline-formula>-hyperideals coincide in a <inline-formula id="inf16"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">J</mml:mi></mml:math></inline-formula>-regular ordered <inline-formula id="inf17"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>Γ</mml:mtext></mml:math></inline-formula>-semihypergroup.</p>