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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: SEMINAR ON ALGEBRA (SALG20)
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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