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Paper Information

Title: 

SOME RESULTS ON WEAK ARMENDARIZ RINGS

Type: PAPER
Author(s): ABOU TALEBI N.H.,HASHEMI EBRAHIM*
 
 *ISLAMIC AZAD UNIVERSITY, SHAHROOD BRANCH, SHAHROOD UNIVERSITY OF TECHNOLOGY
 
Name of Seminar: IRANIAN ALGEBRA SEMINAR
Type of Seminar:  CONFERENCE
Sponsor:  TARBIAT MOALLEM UNIVERSITY, FACULTY OF MATHEMATICAL SCIENCES AND COMPUTER
Date:  2009Volume 20
 
 
Abstract: 

ACCORDING TO Z. LIU AND R. ZHAO [5] A RING R IS CALLED WEAK ARMENDARIZ IF WHENEVER POLYNOMIALS F(X) = A0 + A1X + · · · + AMXM, G(X) = B0 + B1X + · · · + BNXN Î R[X] SATISFY F(X) G(X) = 0, THEN AIBJ 2 NIL(R) FOR ALL I, J. THEY HAVE SHOWN THAT, IF R IS A SEMICOMMUTATIVE RING, THEN THE RING R[X] AND THE RING R[X]/(XN) , WHERE (XN) IS THE IDEAL GENERATED BY XN, AND N IS A POSITIVE INTEGER, ARE WEAK ARMENDARIZ. IN THIS NOTE WE INTRODUCE WEAK ARMENDARIZ IDEALS WHICH ARE A GENERALIZATION OF IDEALS HAVE THE WEAKLY INSERTION OF FACTORS PROPERTY (OR SIMPLY WEAKLY IFP) AND INVESTIGATE THEIR PROPERTIES.

 
Keyword(s): ARMENDARIZ RINGS, WEAK ARMENDARIZ RINGS, SEMICOMMUTATIVE RINGS, WEAKLY SEMICOMMUTATIVE RINGS
 
 
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