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Insertion-of-factors-property, which was introduced by Bell, has a role in the study of various sorts of zero-divisors in noncommutative rings. We in this note consider this property in the case that factors are restricted to maximal ideals. A ring is called IMIP when it satisfies such property. It is shown that the Dorroh extension of A by K is an IMIP ring if and only if A is an IFP ring without identity, where A is a nil algebra over a field K. The structure of an IMIP ring is studied in relation to various kinds of rings which have roles in noncommutative ring theory.
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참고문헌 (17)
참고문헌 신청
A. Smoktunowicz / 2002 / A simple nil ring exists / Comm. Algebra 30 (1) : 27 ~ 59
C. Huh / 2002 / Armendariz rings and semicommutative rings / Comm. Algebra 30 (2) : 751 ~ 761
D. D. Anderson / 1998 / Armendariz rings and Gaussian rings / Comm. Algebra 26 (7) : 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
C. Huh / 2002 / Armendariz rings and semicommutative rings / Comm. Algebra 30 (2) : 751 ~ 761
D. D. Anderson / 1998 / Armendariz rings and Gaussian rings / Comm. Algebra 26 (7) : 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
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