Abstract
An ideal I of an exchange ring R is strongly separative provided that for any A,B ∈ FP(R), A⊕ A≅ A⊕ B ↠ A≅ B. If I is a strongly separative ideal of an exchange ring R, then each a ∈ R satisfying is unit-regular. The converse is true for regular ideals. Furthermore, we prove that strong separativity for such regular ideals can be determined only by one-sided units. Clean property of elements in strongly separative ideals of exchange rings is also studied.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.