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作 者:Cang Wu Jianlong Chen
机构地区:[1]School of Mathematics,Southeast University,Nanjing 210096,China
出 处:《Algebra Colloquium》2024年第4期549-558,共10页代数集刊(英文版)
基 金:National Natural Science Foundation of China(Nos.12171083,11871145 and 12071070);Qing Lan Project of Jiangsu Province,and the Postgraduate Research and Practice Innovation Program of Jiangsu Province(No.KYCX21_0078).
摘 要:We give some new characterizations of strongly one-sided(b,c)-invertibility of elements in rings,and establish the relations between one-sided(b,c)-inverses and strongly one-sided(b,c)-inverses.When b=c,Kaplansky's theorem on the number of one-sided inverses is generalized to the case of strongly one-sided(b,c)-inverses.Moreover,we give some new characterizations of Dedekind-finite rings from the viewpoint of(b,c)-finiteness,and thus answer a question in[L.Wang,D.Mosic,The one-sided inverse along two elements in rings,Linear Multilinear Algebra 69(13)(2021)2410-2422].
关 键 词:(b c)-inverse strongly left(b c)-inverse regularity (b c)-finiteness Dedekind-finite ring
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