Algebraic structures | Lattice theory
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). An example is given by the power set of a set, partially ordered by inclusion, for which the supremum is the union and the infimum is the intersection. Another example is given by the natural numbers, partially ordered by divisibility, for which the supremum is the least common multiple and the infimum is the greatest common divisor. Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities. Since the two definitions are equivalent, lattice theory draws on both order theory and universal algebra. Semilattices include lattices, which in turn include Heyting and Boolean algebras. These lattice-like structures all admit order-theoretic as well as algebraic descriptions. The sub-field of abstract algebra that studies lattices is called lattice theory. (Wikipedia).
The elements of a set can be ordered by a relation. Some relation cause proper ordering and some, partial ordering. Have a look at some examples.
From playlist Abstract algebra
Definition of the Order of an Element in a Group and Multiple Examples
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of the Order of an Element in a Group and Multiple Examples
From playlist Abstract Algebra
Order of Elements in a Group | Abstract Algebra
We introduce the order of group elements in this Abstract Algebra lessons. We'll see the definition of the order of an element in a group, several examples of finding the order of an element in a group, and we will introduce two basic but important results concerning distinct powers of ele
From playlist Abstract Algebra
Orders on Sets: Part 1 - Partial Orders
This was recorded as supplemental material for Math 115AH at UCLA in the spring quarter of 2020. In this video, I discuss the concept and definition of a partial order.
From playlist Orders on Sets
Groups in abstract algebra examples
In this tutorial I discuss two more examples of groups. The first contains four elements and they are the four fourth roots of 1. The second contains only three elements and they are the three cube roots of 1. Under the binary operation of multiplication, these sets are in fact groups.
From playlist Abstract algebra
15 Properties of partially ordered sets
When a relation induces a partial ordering of a set, that set has certain properties with respect to the reflexive, (anti)-symmetric, and transitive properties.
From playlist Abstract algebra
Finding the Order of Group Elements | Abstract Algebra
We go over example problems of finding the order of an element in a group, both with finite order and elements with infinite order. The first example is the additive group of integers mod 10, then we look at the multiplicative reals, then the additive reals, then the symmetric group S4, th
From playlist Abstract Algebra
Lattice Structures in Ionic Solids
We've learned a lot about covalent compounds, but we haven't talked quite as much about ionic compounds in their solid state. These will adopt a highly ordered and repeating lattice structure, but the geometry of the lattice depends entirely on the types of ions and their ratio in the chem
From playlist General Chemistry
Set Theory 1.4 : Well Orders, Order Isomorphisms, and Ordinals
In this video, I introduce well ordered sets and order isomorphisms, as well as segments. I use these new ideas to prove that all well ordered sets are order isomorphic to some ordinal. Email : fematikaqna@gmail.com Discord: https://discord.gg/ePatnjV Subreddit : https://www.reddit.com/r/
From playlist Set Theory
Melting of three-sublattice and easy-axis antiferromagnets on triangular and kagome lattices
New questions in quantum field theory from condensed matter theory Talk Title : Melting of threesublattice order in easyaxis antiferromagnets on triangular and kagome lattices by Kedar Damle URL: http://www.icts.res.in/discussion_meeting/qft2015/ Description:- The last couple of decade
From playlist New questions in quantum field theory from condensed matter theory
Unified Theory of the Spiral Spin-liquids on Layered Honeycomb, Diamond... by Karlo Penc
PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin für Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In
From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)
Progress and Prospects of Lattice Supersymmetry by David Schaich
PROGRAM Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography (ONLINE) ORGANIZERS: David Berenstein (UCSB), Simon Catterall (Syracuse University), Masanori Hanada (University of Surrey), Anosh Joseph (IISER, Mohali), Jun Nishimura (KEK Japan), David Sc
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography (Online)
Nihar Gargava - Random lattices as sphere packings
In 1945, Siegel showed that the expected value of the lattice-sums of a function over all the lattices of unit covolume in an n-dimensional real vector space is equal to the integral of the function. In 2012, Venkatesh restricted the lattice- sum function to a collection of lattices that h
From playlist Combinatorics and Arithmetic for Physics: Special Days 2022
Alessandra Sarti, Old and new on the symmetry groups of K3 surfaces
VaNTAGe Seminar, Feb 9, 2021
From playlist Arithmetic of K3 Surfaces
Lattice N=4 Supersymmetric Yang--Mills by David Schaich
Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography
What is a Riesz Space? -- MathMajor Seminar
⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn ⭐my other channels⭐ Main Channel: https://www.youtube.com/michaelpennmath non-math podcast: http
From playlist MathMajor Seminar
Lattice Supersymmetric Field Theories (Lecture 3) by David Schaich
PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II
From playlist NUMSTRING 2022
Serge Bouc: Correspondence functors
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Dynamic Ferromagnetic Response of a High Temperature Quantum Antiferromagnet
Discussion Meeting: Quantum entanglement in macroscopic matter URL: http://www.icts.res.in/discussion_meeting/QEM2015/ Dates: Monday 12 Jan, 2015 - Friday 16 Jan, 2015 Description: Condensed matter systems display a wide variety of interesting low temperature phases that are the product
From playlist Discussion Meeting: Quantum entanglement in macroscopic matter
Abstract Algebra | The dihedral group
We present the group of symmetries of a regular n-gon, that is the dihedral group D_n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra