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Let R be a ring, and let Ψ(R) be the ideal generated by the set {x ∈ R | 1 + sxt ∈ R is unit-regular for all s, t ∈ R}. We show that Ψ(R) has “radical-like” property. It is proven that Ψ(R) has stable range one. Thus, diagonal reduction of matrices over such ideal is reduced.
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참고문헌 (8)
참고문헌 신청
A. A. Tuganbaev / 2002 / Rings Close to Regular, Mathematics and its Applications, 545 / Kluwer Academic Publishers
B. Brown / 1950 / The maximal regular ideal of a ring / Proc. Amer. Math. Soc. 1 : 165 ~ 171
K. R. Goodearl / 1984 / Cancellation of low-rank vector bundles / Pacific J. Math. 113 (2) : 289 ~ 302
K. R. Goodearl / 1991 / von Neumann Regular Rings, Second edition / Robert E. Krieger Publishing Co., Inc.
P. Ara / 1997 / Diagonalization of matrices over regular rings / Linear Algebra Appl. 265 : 147 ~ 163
B. Brown / 1950 / The maximal regular ideal of a ring / Proc. Amer. Math. Soc. 1 : 165 ~ 171
K. R. Goodearl / 1984 / Cancellation of low-rank vector bundles / Pacific J. Math. 113 (2) : 289 ~ 302
K. R. Goodearl / 1991 / von Neumann Regular Rings, Second edition / Robert E. Krieger Publishing Co., Inc.
P. Ara / 1997 / Diagonalization of matrices over regular rings / Linear Algebra Appl. 265 : 147 ~ 163
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