Strongly One-Sided(b,c)-Inverses in Rings  

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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 

分 类 号:O153.3[理学—数学]

 

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