Ideal Lattices

2017 ◽  
pp. 59-71
Author(s):  
Sueli I. R. Costa ◽  
Frédérique Oggier ◽  
Antonio Campello ◽  
Jean-Claude Belfiore ◽  
Emanuele Viterbo
Keyword(s):  
Ideal Lattices

scholarly journals Mildly Short Vectors in Cyclotomic Ideal Lattices in Quantum Polynomial Time

2021 ◽  
Vol 68 (2) ◽  
pp. 1-26
Author(s):  
Ronald Cramer ◽  
Léo Ducas ◽  
Benjamin Wesolowski
Keyword(s):  
Polynomial Time ◽  
Ideal Lattices ◽  
Quantum Polynomial

scholarly journals Counting Bounded Elements of a Number Field

2020 ◽  
Author(s):  
Mikołaj Fraczyk ◽  
Gergely Harcos ◽  
Péter Maga
Keyword(s):  
Group Theory ◽  
Number Field ◽  
Geometry Of Numbers ◽  
Combine Group ◽  
Successive Minima ◽  
Ideal Lattices ◽  
Linearly Independent ◽  
Ramification Theory

Abstract We estimate, in a number field, the number of elements and the maximal number of linearly independent elements, with prescribed bounds on their valuations. As a by-product, we obtain new bounds for the successive minima of ideal lattices. Our arguments combine group theory, ramification theory, and the geometry of numbers.

Morita invariants of semirings

2015 ◽  
Vol 15 (02) ◽  
pp. 1650023 ◽  
Author(s):  
Sujit Kumar Sardar ◽  
Sugato Gupta
Keyword(s):  
Morita Equivalence ◽  
Ideal Lattices ◽  
Congruence Lattices

In this paper we revisit that ideal lattices and congruence lattices are preserved by Morita equivalence of semirings which is originally obtained implicitly by Katsov and his co-authors. This is then used to obtain some Morita invariants for semirings.

scholarly journals Well-rounded twists of ideal lattices from real quadratic fields

2019 ◽  
Vol 196 ◽  
pp. 168-196 ◽  
Author(s):  
Mohamed Taoufiq Damir ◽  
David Karpuk
Keyword(s):  
Quadratic Fields ◽  
Real Quadratic Fields ◽  
Ideal Lattices ◽  
Real Quadratic

scholarly journals ON THE PARTITION MONOID AND SOME RELATED SEMIGROUPS

2010 ◽  
Vol 83 (2) ◽  
pp. 273-288 ◽  
Author(s):  
D. G. FITZGERALD ◽  
KWOK WAI LAU
Keyword(s):  
Transformation Semigroup ◽  
Galois Connection ◽  
Inverse Semigroups ◽  
Natural Order ◽  
Binary Relations ◽  
Ideal Lattices ◽  
New Interpretation ◽  
Semigroup Of Transformations ◽  
The Ideal

AbstractThe partition monoid is a salient natural example of a *-regular semigroup. We find a Galois connection between elements of the partition monoid and binary relations, and use it to show that the partition monoid contains copies of the semigroup of transformations and the symmetric and dual-symmetric inverse semigroups on the underlying set. We characterize the divisibility preorders and the natural order on the (straight) partition monoid, using certain graphical structures associated with each element. This gives a simpler characterization of Green’s relations. We also derive a new interpretation of the natural order on the transformation semigroup. The results are also used to describe the ideal lattices of the straight and twisted partition monoids and the Brauer monoid.

scholarly journals Authenticated Key Exchange from Ideal Lattices

2015 ◽  
pp. 719-751 ◽  
Author(s):  
Jiang Zhang ◽  
Zhenfeng Zhang ◽  
Jintai Ding ◽  
Michael Snook ◽  
Özgür Dagdelen
Keyword(s):  
Key Exchange ◽  
Authenticated Key Exchange ◽  
Ideal Lattices

Cevian properties in ideal lattices of Abelian ℓ-groups

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Miroslav Ploščica
Keyword(s):  
Distributive Lattice ◽  
Recent Result ◽  
Ideal Lattices ◽  
Ordered Groups ◽  
Lattice Ordered Groups ◽  
Spectral Spaces ◽  
Abelian Lattice

Abstract We consider the problem of describing the lattices of compact ℓ {\ell} -ideals of Abelian lattice-ordered groups. (Equivalently, describing the spectral spaces of Abelian lattice-ordered groups.) It is known that these lattices have countably based differences and admit a Cevian operation. Our first result says that these two properties are not sufficient: there are lattices having both countably based differences and Cevian operations, which are not representable by compact ℓ {\ell} -ideals of Abelian lattice-ordered groups. As our second result, we prove that every completely normal distributive lattice of cardinality at most ℵ 1 {\aleph_{1}} admits a Cevian operation. This complements the recent result of F. Wehrung, who constructed a completely normal distributive lattice having countably based differences, of cardinality ℵ 2 {\aleph_{2}} , without a Cevian operation.

Round-Optimal Verifiable Oblivious Pseudorandom Functions from Ideal Lattices

2021 ◽  
pp. 261-289
Author(s):  
Martin R. Albrecht ◽  
Alex Davidson ◽  
Amit Deo ◽  
Nigel P. Smart
Keyword(s):  
Ideal Lattices ◽  
Pseudorandom Functions

scholarly journals Isometries of Ideal Lattices and Hyperkähler Manifolds

2015 ◽  
Vol 2016 (4) ◽  
pp. 963-977 ◽  
Author(s):  
Samuel Boissière ◽  
Chiara Camere ◽  
Giovanni Mongardi ◽  
Alessandra Sarti
Keyword(s):  
Ideal Lattices ◽  
Hyperkähler Manifolds
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