Modular lattice (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Modular lattice" in English language version.

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Dilworth, R. P. (1954), "Proof of a conjecture on finite modular lattices", Annals of Mathematics, Second Series, 60 (2): 359–364, doi:10.2307/1969639, JSTOR 1969639, MR 0063348. Reprinted in Bogart, Kenneth P.; Freese, Ralph; Kung, Joseph P. S., eds. (1990), "Proof of a Conjecture on Finite Modular Lattices", The Dilworth Theorems: Selected Papers of Robert P. Dilworth, Contemporary Mathematicians, Boston: Birkhäuser, pp. 219–224, doi:10.1007/978-1-4899-3558-8_21, ISBN 978-1-4899-3560-1

archive.org

Modular element has been varying defined by different authors to mean right modular (Stern (1999, p. 74)), left modular (Orlik & Terao (1992, Definition 2.25)), both left and right modular (or dual right modular) (Sagan (1999), Schmidt (1994, p. 43)), or satisfying a modular rank condition (Stanley (2007, Definition 4.12)). These notions are equivalent in a semimodular lattice, but not in general. Stern, Manfred (1999), Semimodular lattices, Cambridge University Press, ISBN 978-0-521-46105-4 Orlik, Peter; Terao, Hiroaki (1992), Arrangements of Hyperplanes, Grundlehren der mathematischen Wissenschaften, vol. 300, Springer-Verlag, doi:10.1007/978-3-662-02772-1 Sagan, Bruce (1999), "Why the characteristic polynomial factors", Bulletin of the American Mathematical Society, 36 (2): 113–133, arXiv:math/9812136, doi:10.1090/S0273-0979-99-00775-2 Schmidt, Roland (1994), Subgroup lattices of groups, de Gruyter Expositions in Mathematics, vol. 14, Walter de Gruyter & Co., doi:10.1515/9783110868647, ISBN 3-11-011213-2 Stanley, Richard P. (2007), "An Introduction to Hyperplane Arrangements", Geometric combinatorics, IAS/Park City Mathematics Series, vol. 13, American Mathematical Society, pp. 389–496, ISBN 978-0-8218-3736-8

arxiv.org

Modular element has been varying defined by different authors to mean right modular (Stern (1999, p. 74)), left modular (Orlik & Terao (1992, Definition 2.25)), both left and right modular (or dual right modular) (Sagan (1999), Schmidt (1994, p. 43)), or satisfying a modular rank condition (Stanley (2007, Definition 4.12)). These notions are equivalent in a semimodular lattice, but not in general. Stern, Manfred (1999), Semimodular lattices, Cambridge University Press, ISBN 978-0-521-46105-4 Orlik, Peter; Terao, Hiroaki (1992), Arrangements of Hyperplanes, Grundlehren der mathematischen Wissenschaften, vol. 300, Springer-Verlag, doi:10.1007/978-3-662-02772-1 Sagan, Bruce (1999), "Why the characteristic polynomial factors", Bulletin of the American Mathematical Society, 36 (2): 113–133, arXiv:math/9812136, doi:10.1090/S0273-0979-99-00775-2 Schmidt, Roland (1994), Subgroup lattices of groups, de Gruyter Expositions in Mathematics, vol. 14, Walter de Gruyter & Co., doi:10.1515/9783110868647, ISBN 3-11-011213-2 Stanley, Richard P. (2007), "An Introduction to Hyperplane Arrangements", Geometric combinatorics, IAS/Park City Mathematics Series, vol. 13, American Mathematical Society, pp. 389–496, ISBN 978-0-8218-3736-8

doi.org

Blyth, T. S. (2005). "Modular lattices". Lattices and Ordered Algebraic Structures. Universitext. London: Springer. Theorem 4.4. doi:10.1007/1-84628-127-X_4. ISBN 978-1-85233-905-0.
Blyth, T. S. (2005). "Modular lattices". Lattices and Ordered Algebraic Structures. Universitext. London: Springer. p. 65. doi:10.1007/1-84628-127-X_4. ISBN 978-1-85233-905-0.
Dilworth, R. P. (1954), "Proof of a conjecture on finite modular lattices", Annals of Mathematics, Second Series, 60 (2): 359–364, doi:10.2307/1969639, JSTOR 1969639, MR 0063348. Reprinted in Bogart, Kenneth P.; Freese, Ralph; Kung, Joseph P. S., eds. (1990), "Proof of a Conjecture on Finite Modular Lattices", The Dilworth Theorems: Selected Papers of Robert P. Dilworth, Contemporary Mathematicians, Boston: Birkhäuser, pp. 219–224, doi:10.1007/978-1-4899-3558-8_21, ISBN 978-1-4899-3560-1
Modular element has been varying defined by different authors to mean right modular (Stern (1999, p. 74)), left modular (Orlik & Terao (1992, Definition 2.25)), both left and right modular (or dual right modular) (Sagan (1999), Schmidt (1994, p. 43)), or satisfying a modular rank condition (Stanley (2007, Definition 4.12)). These notions are equivalent in a semimodular lattice, but not in general. Stern, Manfred (1999), Semimodular lattices, Cambridge University Press, ISBN 978-0-521-46105-4 Orlik, Peter; Terao, Hiroaki (1992), Arrangements of Hyperplanes, Grundlehren der mathematischen Wissenschaften, vol. 300, Springer-Verlag, doi:10.1007/978-3-662-02772-1 Sagan, Bruce (1999), "Why the characteristic polynomial factors", Bulletin of the American Mathematical Society, 36 (2): 113–133, arXiv:math/9812136, doi:10.1090/S0273-0979-99-00775-2 Schmidt, Roland (1994), Subgroup lattices of groups, de Gruyter Expositions in Mathematics, vol. 14, Walter de Gruyter & Co., doi:10.1515/9783110868647, ISBN 3-11-011213-2 Stanley, Richard P. (2007), "An Introduction to Hyperplane Arrangements", Geometric combinatorics, IAS/Park City Mathematics Series, vol. 13, American Mathematical Society, pp. 389–496, ISBN 978-0-8218-3736-8
Dedekind, Richard (1900), "Über die von drei Moduln erzeugte Dualgruppe", Mathematische Annalen, 53 (3): 371–403, doi:10.1007/BF01448979, S2CID 122529830

jstor.org

Dilworth, R. P. (1954), "Proof of a conjecture on finite modular lattices", Annals of Mathematics, Second Series, 60 (2): 359–364, doi:10.2307/1969639, JSTOR 1969639, MR 0063348. Reprinted in Bogart, Kenneth P.; Freese, Ralph; Kung, Joseph P. S., eds. (1990), "Proof of a Conjecture on Finite Modular Lattices", The Dilworth Theorems: Selected Papers of Robert P. Dilworth, Contemporary Mathematicians, Boston: Birkhäuser, pp. 219–224, doi:10.1007/978-1-4899-3558-8_21, ISBN 978-1-4899-3560-1

semanticscholar.org

api.semanticscholar.org

Dedekind, Richard (1900), "Über die von drei Moduln erzeugte Dualgruppe", Mathematische Annalen, 53 (3): 371–403, doi:10.1007/BF01448979, S2CID 122529830

springer.com

link.springer.com

Blyth, T. S. (2005). "Modular lattices". Lattices and Ordered Algebraic Structures. Universitext. London: Springer. Theorem 4.4. doi:10.1007/1-84628-127-X_4. ISBN 978-1-85233-905-0.
Blyth, T. S. (2005). "Modular lattices". Lattices and Ordered Algebraic Structures. Universitext. London: Springer. p. 65. doi:10.1007/1-84628-127-X_4. ISBN 978-1-85233-905-0.

stackexchange.com

math.stackexchange.com

"Why are modular lattices important?". Mathematics Stack Exchange. Retrieved 2018-09-17.

tu-bs.de

digisrv-1.biblio.etc.tu-bs.de

Dedekind, Richard (1897), "Über Zerlegungen von Zahlen durch ihre grössten gemeinsamen Theiler" (PDF), Festschrift der Herzogl. Technischen Hochschule Carolo-Wilhelmina bei Gelegenheit der 69. Versammlung Deutscher Naturforscher und Ärzte in Braunschweig, Friedrich Vieweg und Sohn

uni-goettingen.de

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Dedekind, Richard (1900), "Über die von drei Moduln erzeugte Dualgruppe", Mathematische Annalen, 53 (3): 371–403, doi:10.1007/BF01448979, S2CID 122529830