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.
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