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Armendariz rings. (English) Zbl 0960.16038

From the introduction: It is shown that every \(n\)-by-\(n\) full matrix ring over any ring is not Armendariz, when \(n\geq 2\).

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)
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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
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