期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2009
卷号：2009
DOI：10.1155/2009/696737
出版社：Hindawi Publishing Corporation
摘要：We characterize dependent elements of a commuting derivation 𝑑 on a semiprime ring 𝑅 and investigate a decomposition of 𝑅 using dependent elements of 𝑑. We show that there exist ideals 𝑈 and 𝑉 of 𝑅 such that 𝑈⊕𝑉 is an essential ideal of 𝑅, 𝑈∩𝑉={0}, 𝑑=0 on 𝑈, 𝑑(𝑉)⊆𝑉, and 𝑑 acts freely on 𝑉.
