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 41
- Downloads 0
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.
Relative determinant of a bilinear module
The aim of the paper is to generalize the (ultra-classical) notion of the determinant of a bilinear form to the class of bilinear forms on projective modules without assuming that the determinant bundle of the module is...
Jordan numbers, Stirling numbers and sums of powers
In the paper a new combinatorical interpretation of the Jordan numbers is presented. Binomial type formulae connecting both kinds of numbers mentioned in the title are given. The decomposition of the product of polynomia...
On the intersection graphs of ideals of direct product of rings
In this paper we first calculate the number of vertices and edges of the intersection graph of ideals of direct product of rings and fields. Then we study Eulerianity and Hamiltonicity in the intersection graph of ideals...
SUPERIOR SUBALGEBRAS AND IDEALS OF BCK/BCI-ALGEBRAS
The notions of superior subalgebras and (commutative) superior ideals are introduced, and their relations and related properties are investigated. Conditions for a superior ideal to be commutative are provided.