The current paper studied the concept of right n-derivation satisfying certified conditions on semigroup ideals of near-rings and some related properties. Interesting results have been reached, the most prominent of which are the following: Let M be a 3-prime left near-ring and A_1,A_2,…,A_n are nonzero semigroup ideals of M, if d is a right n-derivation of M satisfies on of the following conditions,
d(u_1,u_2,…,(u_j,v_j ),…,u_n )=0 ∀ 〖 u〗_1 〖ϵA〗_1 ,u_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n ϵA〗_u;
d((u_1,v_1 ),(u_2,v_2 ),…,(u_j,v_j ),…,(u_n,v_n ))=0 ∀u_1,v_1 〖ϵA〗_1,u_2,v_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n,v_n ϵA〗_u ;
d((u_1,v_1 ),(u_2,v_2 ),…,(u_j,v_j ),…,(u_n,v_n ))=(u_j,v_j ) ∀ u_1,v_1 〖ϵA〗_1 ,u_2,v_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n,v_n ϵA〗_u;
If d+d is an n -additive mapping from A_1×A_2×…×A_n to M;
d(u_1,u_2,…,(u_j,v_j ),…,u_n)∈ Z(M) ∀〖 u〗_1 〖ϵA〗_1 ,u_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n ϵA〗_u,;
d((u_1,v_1 ),(u_2,v_2 ),…,(u_j,v_j ),…,(u_n,v_n ))∈ Z(M) ∀ u_1,v_1 〖ϵA〗_1 ,u_2,v_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n,v_n ϵA〗_u;
Then M is a commutative ring.
The Ash'aris and their position on faith, An Ideological Study
Omed AbdulQader rasool
College of Islamic Sciences/Salahaddin University-Erbil
Abstract
The concept of faith is very complex, and there are a lot of talk about it among the major Islamic groups such as the Kharijites, the Mu'tazila, the Jahmiyya and others, because of its great importance, and the worldly and eschatological effects it entails according to the elements of faith such as recognition, ratification and action.
The researcher chose one sect, which is the
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