Rege, M. B.; Chhawchharia, Sima Armendariz rings. (English) Zbl 0960.16038 Proc. Japan Acad., Ser. A 73, No. 1, 14-17 (1997). From the introduction: It is shown that every \(n\)-by-\(n\) full matrix ring over any ring is not Armendariz, when \(n\geq 2\). Cited in 5 ReviewsCited in 204 Documents 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) Keywords:Armendariz rings; full matrix rings PDFBibTeX XMLCite \textit{M. B. Rege} and \textit{S. Chhawchharia}, Proc. Japan Acad., Ser. A 73, No. 1, 14--17 (1997; Zbl 0960.16038) Full Text: DOI References: [1] E. Armendariz : A note on extensions of Baer and P.P. rings. J. Austral. Math. Soc., 18, 470-473 (1974). MR 51, #3224. · Zbl 0292.16009 · doi:10.1017/S1446788700029190 [2] A. Forsythe : Divisors of zero in polynomial rings Amer. Math. Monthly, 50, 7-8 (1943). MR 4, # 129. JSTOR: · Zbl 0060.07704 · doi:10.2307/2303985 [3] Y. Hirano and H. Tominaga: Regular rings, V-rings and their generalizations. Hiroshima Math. J.,9, 137-149 (1979). · Zbl 0413.16015 [4] N. Jacobson : Basic Algebra. W. H. Freeman and Company, vol. 1, San Francisco (1974). · Zbl 0441.16001 [5] N. H. McCoy : Remarks on divisors of zero. Amer. Math. Monthly, 49, 286-295 (1942). MR 3, # 262. JSTOR: · Zbl 0060.07703 · doi:10.2307/2303094 [6] M. Nagata: Local Rings. Interscience (1962). · Zbl 0123.03402 [7] W. R. Scott: Divisors of zero in polynomial rings. Amer. Math. Monthly, 61, 336 (1954). MR 15, # 672. · doi:10.2307/2307474 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.