Insertion-of-Ideal-Factors-Property
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Due to Bell, a ring R is usually said to be IFP if ab = 0 implies aRb = 0 for a; b 2 R. It is shown that if f(x)g(x) = 0 for f(x) = a0+a1x and g(x) = b0+ +bnxn in R[x], then (f(x)R[x])2n+2g(x) = 0. Motivated by this results, we study the structure of the IFP when proper ideals are taken in place of R, introducing the concept of insertion-of- ideal-factors-property (simply, IIFP) as a generalization of the IFP. A ring R will be called an IIFP ring if ab = 0 (for a; b 2 R) implies aIb = 0 for some proper nonzero ideal I of R, where R is assumed to be non- simple. We in this note study the basic structure of IIFP rings.
Abstract
Due to Bell, a ring R is usually said to be IFP if ab = 0 implies aRb = 0 for a; b 2 R. It is shown that if f(x)g(x) = 0 for f(x) = a0+a1x and g(x) = b0+ +bnxn in R[x], then (f(x)R[x])2n+2g(x) = 0. Motivated by this results, we study the structure of the IFP when proper ideals are taken in place of R, introducing the concept of insertion-of- ideal-factors-property (simply, IIFP) as a generalization of the IFP. A ring R will be called an IIFP ring if ab = 0 (for a; b 2 R) implies aIb = 0 for some proper nonzero ideal I of R, where R is assumed to be non- simple. We in this note study the basic structure of IIFP rings.
참고문헌 (10)
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