Characterizations of ordered Γ-Abel-Grassmann's groupoids
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2014, Vol 34, Issue 1
Abstract
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. Keywords: ordered Γ-AG-groupoids, Γ-ideals, regular Γ-AG∗∗-groupoids. 2010 Mathematics Subject Classification: 20M10, 20N99.
Authors and Affiliations
Madad Khan, Venus Amjid, Gul Zaman, Naveed Yaqoob
Keywords
Related Articles
- EP ID EP168235
- DOI -
- Views 22
- Downloads 0
SOME RESULTS OF REVERSE DERIVATION ON PRIME AND SEMIPRIME Γ-RINGS
In the present paper, it is introduced the definition of a reverse derivation on a Γ-ring M. It is shown that a mapping derivation on a semiprime Γ-ring M is central if and only if it is reverse derivation. Also it is sh...
Some properties of the zero divisor graph of a commutative ring
Let Γ(R) be the zero divisor graph for a commutative ring with identity. The k-domination number and the 2-packing number of Γ(R), where R is an Artinian ring, are computed. k-dominating sets and 2-packing sets for the z...
Completely Archimedean Semirings
In this paper we give a structural description of completely Archimedean semirings which is an extension of the structure theorem of completely Archimedean semigroups.
IF-FILTERS OF PSEUDO-BL-ALGEBRAS
Characterizations of IF-filters of a pseudo-BL-algebra are established. Some related properties are investigated. The notation of prime IF- filters and a characterization of a pseudo-BL-chain are given. Homomorphisms of...
ON PERFECTNESS OF INTERSECTION GRAPH OF IDEALS OF Zn
In this short paper, we characterize the positive integers n for which intersection graph of ideals of Zn is perfect.