Characterizations of ordered Γ-Abel-Grassmann's groupoids

• Autorzy: Madad Khan , Venus Amjid , Gul Zaman , Naveed Yaqoob
• Języki publikacji: EN

Abstrakty

EN

In this paper, we introduced the concept of ordered Γ-AG-groupoids, Γ-ideals and some classes in ordered Γ-AG-groupoids. We have shown that every Γ-ideal in an ordered Γ-AG**-groupoid S is Γ-prime if and only if it is Γ-idempotent and the set of Γ-ideals of S is Γ-totally ordered under inclusion. We have proved that the set of Γ-ideals of S form a semilattice, also we have investigated some classes of ordered Γ-AG**-groupoid and it has shown that weakly regular, intra-regular, right regular, left regular, left quasi regular, completely regular and (2,2)-regular ordered Γ-AG**-groupoids coincide. Further we have proved that every intra-regular ordered Γ-AG**-groupoid is regular but the converse is not true in general. Furthermore we have shown that non-associative regular, weakly regular, intra-regular, right regular, left regular, left quasi regular, completely regular, (2,2)-regular and strongly regular Γ-AG*-groupoids do not exist.

Słowa kluczowe

EN

ordered Γ-AG-groupoids; Γ-ideals; regular Γ-AG**-groupoids

Kategorie tematyczne

• 20M10: General structure theory
• 20N99: None of the above, but in this section

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2014
• Tom: 34
• Numer: 1
• Strony: 55-73

Daty

wydano

2014

otrzymano

2013-08-09

poprawiono

2014-01-24

Twórcy

autor

Madad Khan

• Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan

autor

Venus Amjid

• Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan

autor

Gul Zaman

• Department of Mathematics, University of Malakand, Chakdara, Pakistan

autor

Naveed Yaqoob

• Department of Mathematics,, Quaid-i-Azam University, Islamabad, Pakistan

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Identyfikatory

DOI

10.7151/dmgaa.1217