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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2014.1
- 수록면
- 617 - 623 (7page)
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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.
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참고문헌 (10)
참고문헌 신청
C. Huh / 2002 / Armendariz rings and semicommutative rings / Comm. Algebra 30 : 751 ~ 761
D.D. Anderson / 1998 / Armendariz rings and Gaussian rings / Comm. Algebra 26 : 2265 ~ 2272
E.P. Armendariz / 1974 / A note on extensions of Baer and P.P.-rings / J. Austral. Math. Soc 18 : 470 ~ 473
G. Shin / 1973 / Prime ideals and sheaf representation of a pseudo symmetric ring / Trans. Amer. Math. Soc 184 : 43 ~ 60
H.E. Bell / 1970 / Near-rings in which each element is a power of itself / Bull. Austral. Math. Soc 2 : 363 ~ 368
D.D. Anderson / 1998 / Armendariz rings and Gaussian rings / Comm. Algebra 26 : 2265 ~ 2272
E.P. Armendariz / 1974 / A note on extensions of Baer and P.P.-rings / J. Austral. Math. Soc 18 : 470 ~ 473
G. Shin / 1973 / Prime ideals and sheaf representation of a pseudo symmetric ring / Trans. Amer. Math. Soc 184 : 43 ~ 60
H.E. Bell / 1970 / Near-rings in which each element is a power of itself / Bull. Austral. Math. Soc 2 : 363 ~ 368
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