Results 251 to 260 of about 409,221 (291)

Nil Rings Satisfying Certain Chain Conditions

Canadian Journal of Mathematics, 1964
In general, given the fact that every element in a ring is nilpotent, one cannot conclude that the ring itself is nilpotent. However, there are theorems which do assert that, in the presence of certain side conditions, nil implies nilpotent. We shall prove some theorems of this nature here; among them they contain or subsume many of the earlier known ...
Herstein, I. N., Small, Lance
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Ring–Chain Equilibria

1989
Cyclic species are amazingly common amongst the products from polymerization reactions and occur in many different circumstances. Step reaction polymerization almost invariably leads to a sizeable fraction of cyclics of various sizes besides linear chains, and a considerable portion of a high molecular weight material may consist of rings.
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Rings with Chain Conditions

2014
Chapter 7 continues to develop the theory of rings and studies chain conditions for ideals of a ring. The motivation came from an interesting property of the ring of integers Z that its every ascending chain of ideals terminates. This interesting property of Z was first recognized by the German mathematician Emmy Noether (1882–1935).
Mahima Ranjan Adhikari, Avishek Adhikari
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Electronic structure of heterocyclic ring chain polymers

Synthetic Metals, 1999
The band gaps, ionization potentials and electron affinities of conjugated chain polymers comprising heterocyclic aromatic rings are studied systematically as a function of atomic substitutions with N, O and S using first principles density functional calculations.
Brocks, G., Tol, A.E.M., Tol, Arie
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Solvent‐Catalyzed Ring–Chain–Ring Tautomerization in Axially Chiral Compounds

Chemistry – A European Journal, 2012
AbstractThe mechanism of ring–chain–ring tautomerization and the prominent effect of the solvent environment have been computationally investigated in an effort to explain the enantiomeric interconversion observed in 2‐oxazolidinone derivatives, heterocyclic analogues of biphenyl atropisomers, which were isolated as single stable enantiomers and have ...
Asli, Yildirim, Fethiye Aylin Sungur, Konuklar, Saron, Catak, Veronique, Van Speybroeck, Michel, Waroquier, Ilknur, Dogan, Viktorya, Aviyente   +6 more
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Chain–ring interconversion in metasilicates

J. Chem. Soc., Chem. Commun., 1981
Theoretical studies indicate that lattices of the chain and ring varieties of CaSiO3 fit together with only slight mis-match; high resolution electron microscopic studies of a sample undergoing conversion from chain- to ring-structure, however, indicate that intergrowths do not occur and, instead, the chain structure recrystallises via a glassy phase ...
Wen Shu-Lin, S. Ramdas, D. A. Jefferson
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Right chain rings.

1986
Schriftenreihe des Fachbereichs Mathematik.
Törner, Günter, Bessenrodt, Chr., Brungs, H.H.   +2 more
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Periodic Borromean rings, rods and chains

Acta Crystallographica Section A Foundations and Advances
This article describes periodic polycatenane structures built from interlocked rings in which no two are directly linked. The 2-periodic vertex-, edge- and ring-transitive families of hexagonal Borromean rings are described in detail, and it is shown how these give rise to 1- and 3-periodic ring-transitive (isonemal) families.
Michael O'Keeffe, Michael M. J. Treacy
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Completely Primary Rings: IV. Chain Conditions

The Annals of Mathematics, 1952
In [1], [2] and [3] no chain conditions occur anywhere; the strongest "finiteness condition" which had to be postulated for certain parts of the theory was that the rings have nilpotent radicals. (Square brackets refer to the references; [1], [2] and [3] will again be referred to as CPI, CPII and CPIII.) In the present paper we apply the results of CPI,
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Finite chain rings

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 1973
Clark, W. Edwin, Drake, David A.
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