数学研究通讯

2018, v.34(03) 241-252

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J-clean and Strongly J-clean Rings
J-clean and Strongly J-clean Rings

XIANG YUE-MING;OUYANG LUN-QUN;

摘要(Abstract):

Let R be a ring and J(R) the Jacobson radical. An element a of R is called(strongly) J-clean if there is an idempotent e ∈ R and w ∈ J(R) such that a = e + w(and ew = we). The ring R is called a(strongly) J-clean ring provided that every one of its elements is(strongly) J-clean. We discuss, in the present paper,some properties of J-clean rings and strongly J-clean rings. Moreover, we investigate J-cleanness and strongly J-cleanness of generalized matrix rings. Some known results are also extended.

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基金项目(Foundation): The NSF(2016JJ2050)of Hunan Province

作者(Author): XIANG YUE-MING;OUYANG LUN-QUN;

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