Alfred L. Foster and B. A. Bernstein. Symmetric approach to commutative rings, with duality theorem: Boolean duality as a special case. Duke mathematical journal, vol. 11 (1944), pp. 603–616.

1944 ◽  
Vol 9 (4) ◽  
pp. 97-97
Author(s):  
J. C. C. McKinsey
Keyword(s):  
Duality Theorem ◽  
Commutative Rings ◽  
Mathematical Journal ◽  
Duke Mathematical Journal ◽  
Special Case

RATIONALLY ℵα-COMPLETE COMMUTATIVE RINGS OF QUOTIENTS

2009 ◽  
Vol 08 (05) ◽  
pp. 601-615
Author(s):  
JOHN D. LAGRANGE
Keyword(s):  
Commutative Rings ◽  
Von Neumann ◽  
Von Neumann Regular Rings ◽  
Von Neumann Regular ◽  
Ring Of Quotients ◽  
Rings Of Quotients ◽  
Special Case ◽  
Regular Rings

If {Ri}i ∈ I is a family of rings, then it is well-known that Q(Ri) = Q(Q(Ri)) and Q(∏i∈I Ri) = ∏i∈I Q(Ri), where Q(R) denotes the maximal ring of quotients of R. This paper contains an investigation of how these results generalize to the rings of quotients Qα(R) defined by ideals generated by dense subsets of cardinality less than ℵα. The special case of von Neumann regular rings is studied. Furthermore, a generalization of a theorem regarding orthogonal completions is established. Illustrative example are presented.

scholarly journals The Fourier Algebra for Locally Compact Groupoids

2004 ◽  
Vol 56 (6) ◽  
pp. 1259-1289 ◽  
Author(s):  
Alan L. T. Paterson
Keyword(s):  
Duality Theorem ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Fourier Algebra ◽  
Hilbert Modules ◽  
Locally Compact ◽  
Classical Duality ◽  
Special Case

AbstractWe introduce and investigate using Hilbert modules the properties of the Fourier algebra A(G) for a locally compact groupoid G. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This includes as a special case the classical duality theorem for locally compact groups proved by P. Eymard.

Direct Sums of Torsion-Free Covers

1973 ◽  
Vol 25 (5) ◽  
pp. 1002-1005
Author(s):  
Thomas Cheatham
Keyword(s):  
Direct Product ◽  
Commutative Rings ◽  
Integral Domains ◽  
Direct Sums ◽  
Artinian Rings ◽  
Direct Sum ◽  
Special Case ◽  
Torsion Free

In [4, Theorem 4.1, p. 45], Enochs characterizes the integral domains with the property that the direct product of any family of torsion-free covers is a torsion-free cover. In a setting which includes integral domains as a special case, we consider the corresponding question for direct sums. We use the notion of torsion introduced by Goldie [5]. Among commutative rings, we show that the property “any direct sum of torsion-free covers is a torsion-free cover“ characterizes the semi-simple Artinian rings.

R. Dalbiez. L'idée fondamentale de la combinatoire leibnizienne. Travaux du IXe Congrès International de Philosophie, VI Logique et mathématiques, Actualités scientifiques et industrielles 535, Hermann et Cie, Paris1937, pp. 3–7. - Thomas Greenwood. L'extension de la logique aristotélicienne. Travaux du IXe Congrès International de Philosophie, VI Logique et mathématiques, Actualités scientifiques et industrielles 535, Hermann et Cie, Paris1937, pp. 18–25. - Z. Zawtrski. Importance des recherches logiques et sémantiques pour les théories de la physique contemporaine. Travaux du IXe Congrès International de Philosophie, VI Logique et mathématiques, Actualités scientifiques et industrielles 535, Hermann et Cie, Paris1937, pp. 82–87. - Paulette Février. Les relations d'incertitude d'Heisenberg et la logique. Travaux du IXe Congrès International de Philosophie, VI Logique et mathématiques, Actualités scientifiques et industrielles 535, Hermann et Cie, Paris1937, pp. 88–94. [Cf. II 88.] - R. Catesby Taliaferro. Plato and the liberal arts: a plea for mathematical logic. The new scholasticism, vol. 11 (1937), pp. 297–319. - Arnold F. Emch. Deducibility with respect to necessary and impossible propositions. The journal of symbolic logic, vol. 2 (1937), pp. 78–81. - Garrett Birkhoff. Rings of sets. Duke mathematical journal, vol. 3 (1937), pp. 443–454. - N. H. McCoy and Deane Montgomery. A representation of generalized Boolean rings. Duke mathematical journal, vol. 3 (1937), pp. 455–459. - Gottfried Köthe. Die Theorie der Verbände, ein neuer Versuch zur Grundlegung der Algebra und der projektiven Geometrie. Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 47 (1937), 1. Abteilung, pp. 125–144. - Adolf Fraenkel. Review of Carnap's Logische Syntax der Sprache (35212). Scripta mathematica, vol. 4 (1936), pp. 309–312. - A. P. Ushenko. Review of Carnap's The logical syntax of language. The philosophical review, vol. 46 (1937), pp. 549–553. - L. G. Review of Waismann's Einführung in das mathematische Denken (II 142). Rivista di filosofia, vol. 28 (1937), pp. 283–285. - Wilhelm Ackermann. Review of Bentley's Linguistic analysis of mathematics (4611). Jahrbuch über die Fortschritte der Mathematik, vol. 58I no. 1 (for 1932, pub. 1937), pp. 56–57. - C. G. Hempel. Review of Carnap's Die Antinomien und die Unvollständigkeit der Mathematik (35214). Jahrbuch über die Fortschritte der Mathematik, vol. 60II no. 1 (for 1934, pub. 1936), pp. 843–844. - Wilhelm Ackermann. Review of Quine's A system of logistic (4585). Jahrbuch über die Fortschritte der Mathematik, vol. 60II no. 1 (for 1934, pub. 1936), pp. 845–846. - C. G. Hempel. Review of Quine's Toward a calculus of concepts (I 111). Jahrbuch über die Fortschritte der Mathematik, vol. 62I no. 1 (1936), pp. 35–36. - Th. Skolem. Review of Tarski's Grundzüge des Systemenkalküls (28518, I 71). Jahrbuch über die Fortschritte der Mathematik, vol. 62I no. 1 (1936), pp. 38–39. - Friedrich Bachmann. Reviews of Gentzen's Die Widerspruchsfreiheit der Stufenlogik (I 119) and Die Widerspruchsfreiheit der reinen Zahlentheorie (I 75). Jahrbuch über die Fortschritte der Mathematik, vol. 62I no. 1 (1936), pp. 43–44. - M. Kokoszyńska. Filozofia nauki w Kole Wiedeńskim (Philosophy of science in the Circle of Vienna). Kwartalnik filozoficzny, vol. 13, pp. 151–165, 181–194. - M. Kokoszyńska. Review of Carnap's Testability and meaning (II 49). Kwartalnik filozoficzny, vol. 14, pp. 55–61. - M. Black. Review of Gonseth's Les mathématiques et la réalité (II 45). Mind, n.s. vol. 46 (1937), pp. 538–539. - Review of Carnap's Testability and meaning, part 2 (II 49). Mind, n.s. vol. 46 (1937), p. 546. - Edward Gleason Spaulding. A world of chance, or Whence, whither, and why. The Macmillan Company, New York, 1936, xxxiii+293 pp. - R. Feys. Notions de logistique. Mimeographed. 1st. edn., privately circulated, Brussels 1936, vi+102 pp. 2nd. edn., revised, on sale by the Revue Néoscolastique, Louvain 1937.

1937 ◽  
Vol 2 (4) ◽  
pp. 175-176
Keyword(s):  
New York ◽  
Mathematical Logic ◽  
Philosophy Of Science ◽  
Liberal Arts ◽  
Linguistic Analysis ◽  
Mathematical Journal ◽  
Symbolic Logic ◽  
Duke Mathematical Journal ◽  
Logical Syntax ◽  
Boolean Rings
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