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Hongbo Zhang 《代数通讯》2018,46(2):780-791
A ring R is said to have the finitely generated cancellation property provided that the module isomorphism R⊕B?R⊕C implies B?C for any finitely generated R-modules B and C. It is proved that R has this property is equivalent to the existence of the cancellation matrices over R. Moreover, the structure of such matrices is investigated and finite weakly stable rings are characterized in terms of their cancellation matrices. 相似文献
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In this paper we introduce and study the notion of a graded (strongly) nil clean ring which is group graded. We also deal with extensions of graded (strongly) nil clean rings to graded matrix rings and to graded group rings. The question of when nil cleanness of the component, which corresponds to the neutral element of a group, implies graded nil cleanness of the whole graded ring is examined. Similar question is discussed in the case of groupoid graded rings as well. 相似文献
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Kenny Pruitt 《International Journal of Mathematical Education in Science & Technology》2018,49(6):944-947
The purpose of this paper is to consider analogues of the twin-prime conjecture in various classes within modular rings. 相似文献
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Ivan Bazhov 《Journal of Pure and Applied Algebra》2019,223(6):2530-2542
We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kähler fourfold studied by Beauville and Donagi, and the hyper-Kähler fourfold constructed by Debarre and Voisin in [3]. We exhibit an analog of the notion of “triangle” for these varieties and prove that the 6-dimensional variety of “triangles” is a Lagrangian subvariety in the cube of the constructed hyper-Kähler fourfold. 相似文献
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Ludwig Hackl Dr. Alex R. Petrov Dr. Thomas Bannenberg Dr. Matthias Freytag Prof. Dr. Peter G. Jones Prof. Dr. Matthias Tamm 《Chemistry (Weinheim an der Bergstrasse, Germany)》2019,25(70):16148-16155
The reaction of 1,2-dipiperidinoacetylene ( 1 ) with 0.5 equivalents of SnCl2 or GeCl2⋅dioxane afforded the 1,2,3,4-tetrapiperidino-1,3-cyclobutadiene tin and germanium dichloride complexes 2 a and 2 b , respectively. A competing redox reaction was observed with excess amounts of SnCl2, which produced a tetrapiperidinocyclobutadiene dication with two trichlorostannate(II) counterions. Heating neat 1 to 110 °C for 16 h cleanly produced the dimer 1,3,4,4-tetrapiperidino-3-buten-1-yne ( 3 ); its reaction with stoichiometric amounts of SnCl2 or GeCl2⋅dioxane furnished the 1,3,4,4-tetrapiperidino-1,2-cyclobutadiene tin and germanium dichloride complexes 4 a and 4 b , respectively. Transition-metal complexes containing this novel four-membered cyclic bent allene (CBA) ligand were prepared by reaction of 3 with [(tht)AuCl], [RhCl(CO)2]2, and [(Me3N)W(CO)5] to form [(CBA)AuCl] ( 5 ), [(CBA)RhCl(CO)2] ( 6 ), and [(CBA)W(CO)5] ( 7 ). The molecular structures of all compounds 2 – 7 were determined by X-ray diffraction analyses, and density functional theory (DFT) calculations were carried out to rationalise the formation of 3 and 4 a . 相似文献
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Ralph Stöhr 《代数通讯》2018,46(4):1614-1621
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Simon Müller 《代数通讯》2018,46(11):4978-4984
A quasi-order on a set S is a binary, reflexive and transitive relation on S. In [3], Fakhruddin introduced the notion of (totally) quasi-ordered fields and showed that each such field is either an ordered field or else a valued field. Hence, quasi-ordered fields are very well suited to treat ordered and valued fields simultaneously. The aim of the present paper is to prove that an analogous dichotomy holds for commutative rings with 1 as well. 相似文献