Jordan Ideals and Derivations Satisfying Algebraic Identities

Let N be a 3-prime near-ring with center Z ( N ) and J a nonzero Jordan ideal of N . The aim of this paper is to prove some theorems showing that N must be commutative if it admits a left multiplier F satisfying any one of the following properties: ( i ) F ( J ) ⊆ Z ( N ) , ( i i ) F ( J 2 ) ⊆ Z ( N...

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Published inBulletin of the Iranian Mathematical Society Vol. 44; no. 6; pp. 1543 - 1554
Main Authors Boua, A., Bell, H. E.
Format Journal Article
LanguageEnglish
Published Singapore Springer Singapore 01.12.2018
Subjects
Mathematics
Mathematics and Statistics
Original Paper
Jordan ideals
Primary 16N60
Left multipliers
Secondary 16W25
3-Prime near-rings
16Y30
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Abstract Let N be a 3-prime near-ring with center Z ( N ) and J a nonzero Jordan ideal of N . The aim of this paper is to prove some theorems showing that N must be commutative if it admits a left multiplier F satisfying any one of the following properties: ( i ) F ( J ) ⊆ Z ( N ) , ( i i ) F ( J 2 ) ⊆ Z ( N ) , ( i i i ) F ( i j ) + [ i , j ] ∈ Z ( N ) , ( v i ) F ( i j ) - i j + j i ∈ Z ( N ) , ( v ) F ( i ∘ j ) ∈ Z ( N ) and ( v i ) F ( i ) G ( j ) ∈ Z ( N ) , for all i , j ∈ J . Moreover, we give some examples which show that the hypotheses placed in our results are not superfluous.
AbstractList Let N be a 3-prime near-ring with center Z ( N ) and J a nonzero Jordan ideal of N . The aim of this paper is to prove some theorems showing that N must be commutative if it admits a left multiplier F satisfying any one of the following properties: ( i ) F ( J ) ⊆ Z ( N ) , ( i i ) F ( J 2 ) ⊆ Z ( N ) , ( i i i ) F ( i j ) + [ i , j ] ∈ Z ( N ) , ( v i ) F ( i j ) - i j + j i ∈ Z ( N ) , ( v ) F ( i ∘ j ) ∈ Z ( N ) and ( v i ) F ( i ) G ( j ) ∈ Z ( N ) , for all i , j ∈ J . Moreover, we give some examples which show that the hypotheses placed in our results are not superfluous.
Author Boua, A.
Bell, H. E.
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10.1016/S0304-0208(08)72283-7
10.1080/00927879808826190
10.1142/S1005386715000310
10.5269/bspm.v36i4.32032
10.1155/2008/490316
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Keywords Jordan ideals
Primary 16N60
Left multipliers
Secondary 16W25
3-Prime near-rings
16Y30
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A Boua (106_CR6) 2014; 55
A Boua (106_CR7) 2015; 37
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Snippet Let N be a 3-prime near-ring with center Z ( N ) and J a nonzero Jordan ideal of N . The aim of this paper is to prove some theorems showing that N must be...
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Original Paper
Title Jordan Ideals and Derivations Satisfying Algebraic Identities
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