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- W1977169533 abstract "We proved that an exchange ring R the power-substitution property if and only if any one of the following conditions hold: (1) whenever x ∈ R is regular, there exists some positive integer n such that xI n = xWx for some unit-regular element W ∈ M n (R); (2) whenever x ∈ R is regular, there exist positive integers m, n such that x m I n = x m Wx m for some unit-regular element W ∈ M n (R); (3) whenever x = xyx in R, there exists some positive integer n such that xI n = xyW = Wyx for some unit-regular element W ∈ M n (R); (4) whenever aR + bR = dR in R, there exist some positive integer n and W, Q ∈ M n (R), where W is unit-regular, such that aI n + bQ = dW; (5) whenever a 1 R +···+ a k R = dR in R, where k ≥ 1, there exist some positive integer n and unit-regular elements W 1, …, W k ∈ M n (R) such that a 1 W 1 +···+ a k W k = dI n ; (6) whenever a 1 R +···+ a k R = dR in R, where k ≥ 1, there exist positive integers m, n and unit-regular elements W 1, …, W k ∈ M n (R) such that . These results, by..." @default.
- W1977169533 created "2016-06-24" @default.
- W1977169533 creator A5086875634 @default.
- W1977169533 date "2008-05-27" @default.
- W1977169533 modified "2023-09-22" @default.
- W1977169533 title "Power-Substitution and Exchange Rings" @default.
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- W1977169533 doi "https://doi.org/10.1080/00927870801952835" @default.
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