Lee, Tsiu-Kwen; Zhou, Yiqiang Armendariz and reduced rings. (English) Zbl 1068.16037 Commun. Algebra 32, No. 6, 2287-2299 (2004). 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. Reviewer: Xue Weimin (Fujian) Cited in 2 ReviewsCited in 51 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) 16S20 Centralizing and normalizing extensions Keywords:Armendariz rings; reduced rings; matrix rings; trivial extensions Citations:Zbl 0960.16038 PDFBibTeX XMLCite \textit{T.-K. Lee} and \textit{Y. Zhou}, Commun. Algebra 32, No. 6, 2287--2299 (2004; Zbl 1068.16037) Full Text: DOI References: [1] DOI: 10.1080/00927879808826274 · Zbl 0915.13001 · doi:10.1080/00927879808826274 [2] DOI: 10.1017/S1446788700029190 · Zbl 0292.16009 · doi:10.1017/S1446788700029190 [3] DOI: 10.1016/S0022-4049(01)00053-6 · Zbl 1007.16020 · doi:10.1016/S0022-4049(01)00053-6 [4] DOI: 10.1016/S0022-4049(99)00020-1 · Zbl 0982.16021 · doi:10.1016/S0022-4049(99)00020-1 [5] DOI: 10.1081/AGB-120013179 · Zbl 1023.16005 · doi:10.1081/AGB-120013179 [6] Kaplansky I., Mathematics Lecture Notes Series, in: Rings of Operators (1965) [7] DOI: 10.1016/0021-8693(90)90057-U · Zbl 0719.16015 · doi:10.1016/0021-8693(90)90057-U [8] DOI: 10.1006/jabr.1999.8017 · Zbl 0957.16018 · doi:10.1006/jabr.1999.8017 [9] Krempa J., Algebra Colloq. 3 pp 289– (1996) [10] Lee T. K., Houston J. Math. 3 pp 583– (2003) [11] DOI: 10.3792/pjaa.73.14 · Zbl 0960.16038 · doi:10.3792/pjaa.73.14 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.