J4 ›› 2010, Vol. 45 ›› Issue (4): 54-59.
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董珺, 魏杰
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DONG Jun, WEI Jie
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This research is supported by the Scientific Research Fund of Gansu Provincial Education Department (0813B-01)
摘要：
设α是环R的自同态。 称环R为右α-可逆环,如果对任意的a,b∈R若 ab=0, 则 bα(a)=0. 本文讨论了α-可逆环,α-刚性环,可逆环和弱α-Skew Armendariz环的关系。 设R是可逆环和右α-可逆环,证明了:(1)R是弱α-Skew Armendariz环;(2) 对任意的正整数n, R［x］／(xn)是弱α-Skew Armendariz环;(3)若αt=1R, 则R［x;α］是弱Armendariz环.
关键词: α-可逆环；α-刚性环； 弱α-Skew Armendariz环
Abstract:
An endomorphism α of a ring R is called right reversible if whenever ab=0 for a,b∈R,bα(a)=0. A ring R is called right α-reversible if there exists a right reversible endomorphism α of R. The relations between α-reversible, α-rigid, reversible and weak α-skew Armendariz rings are investigated. And it is proven that for reversible and right α-reversible rings R: (1) R is a weak α-skew Armendariz ring; (2) R［x］／(xn) is a weak α-skew Armendariz ring for any positive integer n; (3) If for some positive integer t, αt=1R, then R［x;α］ is weak Armendarizring.
Key words: α-reversible ring; α-rigid ring; weak α-skew Armendariz ring
董珺, 魏杰. α-可逆环的一点注记[J]. J4, 2010, 45(4): 54-59.
DONG Jun, WEI Jie. A note on α-reversible rings[J]. J4, 2010, 45(4): 54-59.
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