Intra Regular and Interior Ideal in \(\Gamma- Ag^*\)-groupoids


Authors

A. R. Shabani - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran. H. Rasouli - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.


Abstract

Non-associative algebraic structures are of interest to consider for their remarkable properties. In this paper, we generalize the \(AG^*\)-groupoids to \(\Gamma-AG^*\)-groupoids and study their algebraic properties. Among other results, it is shown that every \(\Gamma-AG^*\)-groupoid is left alternative and a \(\Gamma-AG^*\)-groupoid having a left cancellative element is a \(T^1-\Gamma-AG^*\)-groupoid, a \(a\Gamma-AG^*\)-groupoid \(S\) is a \(\Gamma\)-intra-regular if \(S\Gamma a = S\) holds for all \(a \in S\), let \(S\) be a \(\Gamma\)-intra-regular of \(\Gamma-AG^*\)-groupoid then B is a right \(\Gamma\)-ideal of \(S\) if \(B\Gamma S = B\), if S is a \(\Gamma\)-intra-regular of \(\Gamma-AG^*\)-groupoid then \((S\Gamma B)\Gamma S = B\), where \(B\) is a \(\Gamma\)-interior ideal of \(S\), in an \(\Gamma\)-intra-regular of \(\Gamma-AG^*\)-groupoid \(S\) if \(A\) is a \(\Gamma\)-interior ideal of \(S\) then \(A\) is a \(\Gamma\)-bi-ideal of \(S\), in an \(\Gamma\)-intra-regular of \(\Gamma-AG^*\)-groupoid \(S\) if \(A\) is a \(\Gamma\)-interior ideal of \(S\) then \(A\) is a \(\Gamma(1, 2)\)-ideal of \(S\).


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ISRP Style

A. R. Shabani, H. Rasouli, Intra Regular and Interior Ideal in \(\Gamma- Ag^*\)-groupoids, Journal of Mathematics and Computer Science, 16 (2016), no. 1, 81-87

AMA Style

Shabani A. R., Rasouli H., Intra Regular and Interior Ideal in \(\Gamma- Ag^*\)-groupoids. J Math Comput SCI-JM. (2016); 16(1):81-87

Chicago/Turabian Style

Shabani, A. R., Rasouli, H.. "Intra Regular and Interior Ideal in \(\Gamma- Ag^*\)-groupoids." Journal of Mathematics and Computer Science, 16, no. 1 (2016): 81-87


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