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Nil 3-Armendariz Rings
1Department of Mathematics, Northwest Normal University, Lanzhou, China 2Department of Mathematics, Khartoum University, Omdurman, Sudan
1Department of Mathematics, Northwest Normal University, Lanzhou, China 2Department of Mathematics, Khartoum University, Omdurman, Sudan
Department of Mathematics, Northwest Normal University, Lanzhou, China
- 1 1Department of Mathematics, Northwest Normal University, Lanzhou, China 2Department of Mathematics, Khartoum University, Omdurman, Sudan
- 2 1Department of Mathematics, Northwest Normal University, Lanzhou, China 2Department of Mathematics, Khartoum University, Omdurman, Sudan
- 3 Department of Mathematics, Northwest Normal University, Lanzhou, China
Advances in Pure Mathematics·Volume 03 (2013)·Pages 703–708·Published 28 November 2013·DOI10.4236/apm.2013.39096
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Abstract
We introduce nil 3-Armendariz rings, which are generalization of 3-Armendariz rings and nil Armendaiz rings and investigate their properties. We show that a ring R is nil 3-Armendariz ring if and only if for any , T n ( R ) is nil 3-Armendariz ring . Also we prove that a right Ore ring R is nil 3-Armendariz if and only if so is Q , where Q is the classical right quotient ring of R . With the help of this result , we can show that a commutative ring R is nil 3-Armendariz if and only if the total quotient ring of R is nil 3-Armendariz.
KeywordsArmendariz Ring3-Armendariz RingNil Armendariz RingNil 3-Armendariz Ring
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