Uniquely exchange rings
Rashedi, F.
Publications de l'Institut Mathematique (DOI: 10.2298/pim2226053r)
Generated on June 30, 2025
Uniquely exchange rings
Abstract
<jats:p>An associative ring with unity is called exchange if every element is
exchange, i.e., there exists an idempotent e ? aR such that 1?e ? (1?a)R; if
this representation is unique for every element, we call the ring uniquely
exchange. We give a complete description of uniquely exchange rings.</jats:p>
Publications de l'Institut Mathematique 2022 Volume 112, Issue 126, Pages: 53-57
https://doi.org/10.2298/PIM2226053R Full text ( 106 KB) Uniquely exchange rings Rashedi
Fatemeh (Department of Mathematics, Technical and Vocational university (TVU), Tehran,
Iran), f-rashedi@tvu.ac.ir An associative ring with unity is called exchange if every element is
exchange, i.e., there exists an idempotent e ∈ aR such that 1−e ∈ (1−a)R; if
this representation is unique for every element, we call the ring uniquely
exchange. We give a complete description of uniquely exchange rings. Keywords: exchange
ring, uniquely exchange ring
Publications de l'Institut Mathematique 2022 Volume 112, Issue 126, Pages: 53-57
https://doi.org/10.2298/PIM2226053R Full text ( 106 KB)
Rashedi Fatemeh (Department of Mathematics, Technical and Vocational university (TVU),
Tehran, Iran), f-rashedi@tvu.ac.ir
An associative ring with unity is called exchange if every element is
exchange, i.e., there exists an idempotent e ∈ aR such that 1−e ∈ (1−a)R; if
this representation is unique for every element, we call the ring uniquely
exchange. We give a complete description of uniquely exchange rings.