Communications of the
Korean Mathematical Society CKMS

This article concerns a generalization of Armendariz rings that is done by restricting the degree to one. We shall call such rings, as to satisfy this property, {\it partial-Armendariz}. We first show that partial-Armendariz rings are between Armendariz rings and weak Armendariz rings. The basic structures of partial-Armendariz rings are investigated, and the relations between partial-Armendariz rings and near related ring properties are also studied.

Keywords: partial-Armendariz ring, Armendariz ring, weak Armendariz ring, polynomial ring, reduced ring, matrix ring

MSC numbers: 16S36, 16S50, 16N40

Supported by: The second named author was supported by the National Natural Science Foundation of China(11361063). The third named author was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government (MSIP; Ministry of Science, ICT & Future Planning) (No. 2017R1C1B5017863).