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J-Clean and Strongly J-Clean Rings

J-Clean and Strongly J-Clean Rings

Year:    2018

Author:    Yueming Xiang, Lunqun Ouyang

Communications in Mathematical Research , Vol. 34 (2018), Iss. 3 : pp. 241–252

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 eR and wJ(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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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.13447/j.1674-5647.2018.03.06

Communications in Mathematical Research , Vol. 34 (2018), Iss. 3 : pp. 241–252

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    J-clean ring strongly J-clean ring generalized matrix ring

Author Details

Yueming Xiang Email

Lunqun Ouyang Email