INSERTION-OF-FACTORS-PROPERTY WITH FACTORS MAXIMAL IDEALS
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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.
Abstract
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.
참고문헌 (17)
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