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）...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.展开更多
文摘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.
