Is there a name for a distributive lattice with only two (nonequal) elements, 1 and 0, corresponding to top and bottom, respectively? I was thinking of calling it a trivial lattice, but a trivial lattice should probably just have one element.
2026-04-03 10:38:28.1775212708
What is the name for a distributive lattice with only two elements, top and bottom?
108 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in TERMINOLOGY
- The equivalent of 'quantum numbers' for a mathematical problem
- Does approximation usually exclude equality?
- Forgot the name of a common theorem in calculus
- Name of some projection of sphere onto $\mathbb{R}^2$
- What is $x=5$ called??
- Is there a name for this operation? $f(a, b) = a + (1 - a)b$
- When people say "an algebra" do they always mean "an algebra over a field"?
- What is the term for "in one $n$-space"?
- The product of disjoint cycles
- What about the 'geometry' in 'geometric progression'?
Related Questions in LATTICE-ORDERS
- When a lattice is a lattice of open sets of some topological space?
- How to identify if a given Hasse diagram is a lattice
- How to find the smallest cardinal of a minimal generating set of a lattice
- Finding a poset with a homogeneity property
- Why is the "distributive lattice" structure of domino tilings significant?
- Two lattice identities
- Quickly determining whether given lattice is a distributive lattice from a given Hasse diagram
- Characteristic of a lattice that subsets contain their meets and joins
- Equalities in Heyting algebras
- Show that $(\operatorname{Up}(P),\subset)$ is a distributive lattice
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
For a name, I would use the two-element chain. Grätzer uses this at least nine times in his book Lattice Theory. Foundation (Birkhäuser/Springer 2011).
Common notations are $C_2$ (used by Grätzer) and $\mathbf{2}$ (used by Stanley in Enumerative Combinatorics, vol. 1).