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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.
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참고문헌 (17)
참고문헌 신청
D.D. Anderson / 1998 / Armendariz rings and gaussian rings / Communications in Algebra 26(7):2265~2272
Ramon Antoine / 2008 / Nilpotent elements and Armendariz rings / Journal of Algebra 319(8):3128~3140
Ramon Antoine / 2010 / Examples of Armendariz Rings / Communications in Algebra 38(11):4130~4143
E. P. Armendariz / 1974 / A note on extensions of Baer and P. P. -rings / J. Austral. Math. Soc 18:470~473
Howard E. Bell / 1970 / Near-rings in which each element is a power of itself / Bulletin of the Australian Mathematical Society 2(3):363~368
Ramon Antoine / 2008 / Nilpotent elements and Armendariz rings / Journal of Algebra 319(8):3128~3140
Ramon Antoine / 2010 / Examples of Armendariz Rings / Communications in Algebra 38(11):4130~4143
E. P. Armendariz / 1974 / A note on extensions of Baer and P. P. -rings / J. Austral. Math. Soc 18:470~473
Howard E. Bell / 1970 / Near-rings in which each element is a power of itself / Bulletin of the Australian Mathematical Society 2(3):363~368
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