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 ...
متن کاملA Note on Rings of Weakly Stable Range One
It is shown that if R and S are Morita equivalent rings then R has weakly stable range 1 (written as wsr(R) = 1) if and only if S has. Let T be the ring of a Morita context (R,S,M,N,ψ, φ) with zero pairings. If wsr(R) = wsr(S) = 1, we prove that T is a weakly stable ring. A ring R is said to have weakly stable range one if aR + bR = R implies that there exists a y ∈ R such that a + by ∈ R is ri...
متن کاملDirect Sum Cancellation for Modules over One-dimensional Rings
Let R be a one-dimensional Noetherian domain with finite normalization R. In the eighties the second-named author and S. Wiegand developed a mechanism for studying the cancellation problem for finitely generated torsion-free R-modules. The key idea, described in [Wie84] and [WW87], is to represent a given torsion-free module M as a pullback: M −→ RM ↓ ↓ M/fM −→ RM/fM ∗This research was initiate...
متن کاملDirect-sum decompositions over one-dimensional Cohen-Macaulay local rings
1 Alberto Facchini, Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Belzoni 7, I-35131 Padova, Italy, [email protected] 2 Wolfgang Hassler, Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstraße 36/IV, A-8010 Graz, Austria, [email protected] 3 Lee Klingler, Department of Mathematical Sciences, Florida Atlanti...
متن کاملJosephson Behavior in Small Normal One-dimensional Rings
where R is the reflection probability for a carrier entering the specimen, at the Fermi energy. Derivations of eq. (1) invoke the unperturbed wave functions of the specimen, illustrated in fig. 1 and consider the current flow and carrier density gradients associated with these. Wave functions representing carriers incident from the reservoir on the right are also taken into account, but not sho...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2016
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2016.02.002