EXCHANGE RINGS SATISFYING UNIT 1-STABLE RANGE
نویسندگان
چکیده
منابع مشابه
Exchange Rings Having Stable Range One
We investigate the sufficient conditions and the necessary conditions on an exchange ring R under which R has stable range one. These give nontrivial generalizations of Theorem 3 of V. P. Camillo and H.-P. Yu (1995), Theorem 4.19 of K. R. Goodearl (1979, 1991), Theorem 2 of R. E. Hartwig (1982), and Theorem 9 of H.-P. Yu (1995). 2000 Mathematics Subject Classification. Primary 16E50, 19B10. An ...
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Let R be a ring with identity 1. We say that R satisfies unit 1-stable range in case ax+b = 1 with a,x,b ∈ R implying that a+bu ∈ U(R). Many authors studied unit 1-stable range such as those of [1, 2, 3, 4, 5, 6]. Following the authors, a ring R satisfies unit 1-stable range for an ideal I provided that ax+b = 1 with a∈ I, x,b ∈ R implying that x+ub ∈U(R) for some unit u∈U(R). Let R = Z/2Z⊕Z/3Z...
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Elementary divisor domains were defined by Kaplansky [I. Kaplansky, Elementary divisors and modules, Trans. Amer. Math. Soc. 66 (1949) 464–491] and generalized to rings with zero-divisors by Gillman and Henriksen [L. Gillman, M. Henriksen, Some remarks about elementary divisor rings, Trans. Amer. Math. Soc. 82 (1956) 362–365]. In [M.D. Larsen, W.J. Lewis, T.S. Shores, Elementary divisor rings a...
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In a recent paper, the first author introduced a general theory of corner rings in noncommutative rings that generalized the classical theory of Peirce decompositions. This theory is applied here to the study of the stable range of rings upon descent to corner rings. A ring is called quasi-duo if every maximal 1-sided ideal is 2-sided. Various new characterizations are obtained for such rings. ...
متن کاملBézout Rings with Almost Stable Range 1 are Elementary Divisor Rings
Abstract. In this article we revisit a problem regarding Bézout domains, namely, whether every Bézout domain is an elementary divisor domain. Elementary divisor domains where defined by Kaplansky [13] and generalized to rings with zero-divisors by Gillman and Henriksen [7]. Later, in [14] it was shown that a domain R is an elementary divisor domain if and only if every finitely presented R-modu...
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ژورنال
عنوان ژورنال: Kyushu Journal of Mathematics
سال: 2000
ISSN: 1340-6116,1883-2032
DOI: 10.2206/kyushujm.54.1