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A ring R is a weakly stable ring provided that aR+bR=R implies
that there exists y∈R such that a+by∈R is right or left
invertible. In this article, we characterize weakly stable rings
by virtue of 2×2 invertible matrices over them. It is
shown that a ring R is a weakly stable ring if and only if for
any A∈GL_2(R), there exist two invertible lower triangular
L and K and an invertible upper triangular U such that
A=LUK, where two of L,U and K have diagonal entries 1.
Related results are also given. These extend the work of Nagarajan
et al.
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참고문헌 (16)
참고문헌 신청
A. A. Tuganbaev / 2002 / Rings Close to Regular / Kluwer Academic Publishers
D. Lu / 2004 / Comparability, stability, and completions of ideals / Comm. Algebra 32 (7) : 2617 ~ 2634
G. Ehrlich / 1976 / Units and one-sided units in regular rings / Trans. Amer. Math. Soc. 216 : 81 ~ 90
H. Chen / 1997 / Comparability of modules over regular rings / Comm. Algebra 25 (11) : 3531 ~ 3543
H. Chen / 2004 / On products of three triangular matrices over associative rings / Linear Algebra Appl. 387 : 297 ~ 311
D. Lu / 2004 / Comparability, stability, and completions of ideals / Comm. Algebra 32 (7) : 2617 ~ 2634
G. Ehrlich / 1976 / Units and one-sided units in regular rings / Trans. Amer. Math. Soc. 216 : 81 ~ 90
H. Chen / 1997 / Comparability of modules over regular rings / Comm. Algebra 25 (11) : 3531 ~ 3543
H. Chen / 2004 / On products of three triangular matrices over associative rings / Linear Algebra Appl. 387 : 297 ~ 311
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