Relevant bibliographies by topics / Lattice of divisibility

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Academic literature on the topic 'Lattice of divisibility'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Lattice of divisibility"

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MOSAK, RICHARD, and MARTIN MOSKOWITZ. "Lattices in a split solvable Lie group." Mathematical Proceedings of the Cambridge Philosophical Society 122, no. 2 (1997): 245–50. http://dx.doi.org/10.1017/s0305004196001582.

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Given a Lie group, it is often useful to have a parametrization of the set of its lattices. In Euclidean space ℝn, for example, each lattice corresponds to a basis, and any lattice is equivalent to the standard integer lattice under an automorphism in GL(n, ℝ). In the nilpotent case, the lattices of the Heisenberg groups are classified, up to automorphisms, by certain sequences of positive integers with divisibility conditions (see [1]). In this paper we will study the set of lattices in a class of simply connected, solvable, but not nilpotent groups G. The construction of G depends on a diago
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Paudel, Lokendra. "Finite intersection of valuation overrings of polynomial rings in at most three variables." Algebra and Discrete Mathematics 37, no. 1 (2024): 106–33. http://dx.doi.org/10.12958/adm1997.

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The group of divisibility of an integral domainis the multiplicative group of nonzero principal fractional ideals ofthe domain and is a partially ordered group under reverse inclusion. We study the group of divisibility of a finite intersection of valuation overrings of polynomial rings in at most three variables and we classify all semilocal lattice-ordered groups which are realizable over k[x1,x2,...,xn] for n≤3.
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Alexander, Bolotin. "The Propositional Lattice of Divisibility and Beal's Conjecture." British Journal of Mathematics & Computer Science 22, no. 2 (2017): 1–8. https://doi.org/10.9734/BJMCS/2017/33315.

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VAN GASSE, BART, CHRIS CORNELIS, GLAD DESCHRIJVER, and ETIENNE E. KERRE. "ON THE PROPERTIES OF A GENERALIZED CLASS OF T-NORMS IN INTERVAL-VALUED FUZZY LOGICS." New Mathematics and Natural Computation 02, no. 01 (2006): 29–41. http://dx.doi.org/10.1142/s1793005706000361.

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Since it does not generate any MTL-algebra (prelinear residuated lattice), the lattice [Formula: see text] of closed subintervals of [0, 1] falls outside the mainstream of research on formal fuzzy logics. However, due to the intimate connection between logical connectives on [Formula: see text] and those on [0, 1], many relevant logical properties can still be maintained, sometimes in a slightly weaker form. In this paper, we focus on a broad class of parametrized t-norms on [Formula: see text]. We derive their corresponding residual implicators, and examine commonly imposed logical properties
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DROSTE, MANFRED, and DIETRICH KUSKE. "Recognizable languages in divisibility monoids." Mathematical Structures in Computer Science 11, no. 6 (2001): 743–70. http://dx.doi.org/10.1017/s0960129501003395.

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We define the class of divisibility monoids that arise as quotients of the free monoid Σ* modulo certain equations of the form ab = cd. These form a much larger class than free partially commutative monoids, and we show, under certain assumptions, that the recognizable languages in these divisibility monoids coincide with c-rational languages. The proofs rely on Ramsey's theorem, distributive lattice theory and on Hashigushi's rank function generalized to these monoids. We obtain Ochmański's theorem on recognizable languages in free partially commutative monoids as a consequence.
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Bolotin, Alexander. "The Propositional Lattice of Divisibility and Beal's Conjecture." British Journal of Mathematics & Computer Science 22, no. 2 (2017): 1–8. http://dx.doi.org/10.9734/bjmcs/2017/33315.

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Glaffig, Clemens, and Ed Waymire. "Infinite divisibility of a bethe lattice ising model." Journal of Statistical Physics 47, no. 1-2 (1987): 185–92. http://dx.doi.org/10.1007/bf01009041.

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Hurd, Spencer. "Divisibility in O-primitive lattice-ordered permutation groups." Order 3, no. 2 (1986): 195–205. http://dx.doi.org/10.1007/bf00390109.

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Chajda, Ivan, and Helmut Länger. "Residuation in non-associative MV-algebras." Mathematica Slovaca 68, no. 6 (2018): 1313–20. http://dx.doi.org/10.1515/ms-2017-0181.

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Abstract It is well known that every MV-algebra can be converted into a residuated lattice satisfying divisibility and the double negation law. In a previous paper the first author and J. Kühr introduced the concept of an NMV-algebra which is a non-associative modification of an MV-algebra. The natural question arises if an NMV-algebra can be converted into a residuated structure, too. Contrary to MV-algebras, NMV-algebras are not based on lattices but only on directed posets and the binary operation need not be associative and hence we cannot expect to obtain a residuated lattice but only an
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NOBLE, ROB. "ASYMPTOTICS OF THE WEIGHTED DELANNOY NUMBERS." International Journal of Number Theory 08, no. 01 (2012): 175–88. http://dx.doi.org/10.1142/s1793042112500108.

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The weighted Delannoy numbers give a weighted count of lattice paths starting at the origin and using only minimal east, north and northeast steps. Full asymptotic expansions exist for various diagonals of the weighted Delannoy numbers. In the particular case of the central weighted Delannoy numbers, certain weights give rise to asymptotic coefficients that lie in a number field. In this paper we apply a generalization of a method of Stoll and Haible to obtain divisibility properties for the asymptotic coefficients in this case. We also provide a similar result for a special case of the diagon
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Dissertations / Theses on the topic "Lattice of divisibility"

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Moura, Andréa Maria Ferreira. "Grupos de Divisibilidade e Reticulados." Universidade Federal da Paraí­ba, 2010. http://tede.biblioteca.ufpb.br:8080/handle/tede/7456.

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Made available in DSpace on 2015-05-15T11:46:24Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 885143 bytes, checksum: 948ed501e70f201fbd41ae588572c5bc (MD5) Previous issue date: 2010-08-03<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>We present in this work a complete classification of the sublattices of (Zn,+, ≥) which are not groups of divisibility. Thus we provide a new class of ordered filtered groups of which are not groups of divisibility. The sublattices presented here generalize the exemples of P.Jaffard and G. G. Bastos<br>Apresentamos nesse trabal
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Book chapters on the topic "Lattice of divisibility"

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Anderson, Marlow, and Todd Feil. "Groups of Divisibility." In Lattice-Ordered Groups. Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2871-8_11.

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Mott, Joe L. "Groups of Divisibility: A Unifying Concept for Integral Domains and Partially Ordered Groups." In Lattice-Ordered Groups. Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-2283-9_5.

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Anderson, Marlow. "Lattice-Ordered Groups of Divisibility: An Expository Introduction." In Ordered Algebraic Structures. Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-2472-7_1.

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Valverde-Albacete, Francisco José, Carmen Peláez-Moreno, Inma P. Cabrera, Pablo Cordero, and Manuel Ojeda-Aciego. "Encoding Non-global Time Representations into the Lattice of Divisibility." In Information Processing and Management of Uncertainty in Knowledge-Based Systems. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-08971-8_11.

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Potter, Michael D. "Lattices." In Sets: An Introduction. Oxford University PressOxford, 1991. http://dx.doi.org/10.1093/oso/9780198533887.003.0009.

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Abstract What we now call the theory of lattices originated in the late nineteenth century from two sources: Dedekind came upon the notion of a Dualgruppe — what is now called a ‘modular lattice’ — in his investigation of the theory of divisibility; the other motivating example is the algebra of classes — theory of logical equivalence of propositions — which was studied by Boole, Schröder, and others. The work we shall be describing in this chapter is almost all the product of research in the 1930s by Birkhoff and Øre. Since then lattices have found natural application in functional analysis,
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Cofman, Judita. "Patterns, related to rational numbers; periodic decimal fractions, repunits, and visible lattice points." In Numbers and Shapes Revisited. Oxford University PressOxford, 1995. http://dx.doi.org/10.1093/oso/9780198534600.003.0003.

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Abstract Numbers expressible as fractions a/b, where a and bare integers and b &amp;gt; 0, are called rational numbers. Each rational number can be expanded as a decimal fraction (e.g. 2/5 = 0.4, 5/3 = 1.666 ... ) with either a finite or infinite number of decimal places. In Sections 3.1 and 3.2 we shall study sequences of digits in decimal expansions of rational numbers; we shall also deduce a divisibility criterion for repunits - important numbers in computer science and coding theory.
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Wolfsdorf, David Conan. "Adjectival Nominalization." In On Goodness. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780190688509.003.0006.

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Chapter 6 focuses on the semantics and metaphysical implications of the semantics of the adjectival nominalization “goodness.” Adjectival nominalizations of the form “F-ness” are almost always mass nouns. The mass noun “goodness” derives gradability of a kind from the gradable adjective that it incorporates. So “goodness” is a gradable adjectival nominalization. Mass nouns are distinguished from count nouns on the basis of two semantic properties, called “semantic cumulativity” and “semantic divisibility.” The denotations of mass nouns are then interpreted in terms of the mereological structur
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