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Armendariz and reduced rings. (English) Zbl 1068.16037

As a generalization of reduced rings, M. B. Rege and S. Chhawchharia [Proc. Japan Acad., Ser. A 73, No. 1, 14-17 (1997; Zbl 0960.16038)] introduced Armendariz rings. The authors obtain a necessary and sufficient condition for a trivial extension to be an Armendariz ring.

MSC:

16S36 Ordinary and skew polynomial rings and semigroup rings
16S50 Endomorphism rings; matrix rings
16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
16S20 Centralizing and normalizing extensions

Citations:

Zbl 0960.16038
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References:

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[11] DOI: 10.3792/pjaa.73.14 · Zbl 0960.16038 · doi:10.3792/pjaa.73.14
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