theory, a complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every element a has a complement, i.e. an element...

called a complemented lattice. A complemented lattice that is also distributive is a Boolean algebra. For a distributive lattice, the complement of x ,...

theory, a pseudocomplement is one generalization of the notion of complement. In a lattice L with bottom element 0, an element x ∈ L is said to have a pseudocomplement...

element is the trivial topology. The lattice of topologies on a set X {\displaystyle X} is a complemented lattice; that is, given a topology τ {\displaystyle...

In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties...

cyclic. Groups whose lattice of subgroups is a complemented lattice are called complemented groups (Zacher 1953), and groups whose lattice of subgroups are...

realm of group theory, the term complemented group is used in two distinct, but similar ways. In (Hall 1937), a complemented group is one in which every subgroup...

complement Two's complement Complement graph Self-complementary graph, a graph which is isomorphic to its complement Complemented lattice Complement of an angle...

Boolean algebra: a complemented distributive lattice. Either of meet or join can be defined in terms of the other and complementation. Module: an abelian...

orthocomplemented lattice is complemented. (def) 8. A complemented lattice is bounded. (def) 9. An algebraic lattice is complete. (def) 10. A complete lattice is bounded...

A lattice is a partially ordered set that is both a meet- and join-semilattice with respect to the same partial order. Algebraically, a lattice is a...

hyperbolas are hyperbolic-orthogonal. Complemented lattice – Bound lattice in which every element has a complement Complemented subspace Hilbert projection theorem –...

matroid. Geometric lattices are complemented, and because of the interval property they are also relatively complemented. Every finite lattice is a sublattice...

Knaster–Tarski theorem Infinite divisibility Heyting algebra Relatively complemented lattice Complete Heyting algebra Pointless topology MV-algebra Ockham algebras:...

corollary of the similar result on complete lattices, as the quotient R/~ need not be a complete lattice for a GCD domain R.[citation needed] If R is...

ring Ring theory Lattice-like Lattice Semilattice Complemented lattice Total order Heyting algebra Boolean algebra Map of lattices Lattice theory Module-like...

relatively complemented lattice). In contrast, the class of all subsets of U, called the power set of U, is a Boolean lattice. The absolute complement described...

operations + (the module spanned by the union of the arguments) and ∩, forms a lattice that satisfies the modular law: Given submodules U, N1, N2 of M such that...

is a complemented lattice, i.e. a Boolean algebra. The same holds for any semilattice when "semilattice" is substituted for "distributive lattice" and...

ring Ring theory Lattice-like Lattice Semilattice Complemented lattice Total order Heyting algebra Boolean algebra Map of lattices Lattice theory Module-like...

To define this, one can note that the fundamental group of the knot complement, or knot group, has a presentation (the Wirtinger presentation) in which...

regular; every x in H is complemented. In this case, the element a→b is equal to ¬a ∨ b. The regular (respectively complemented) elements of any Heyting...

associates) A ¯ A = 1 {\displaystyle {\overline {A}}A=1} (2 is a complemented lattice, with an upper bound of 1)   A 0 = A {\displaystyle \ A0=A} (0 is...

ring Ring theory Lattice-like Lattice Semilattice Complemented lattice Total order Heyting algebra Boolean algebra Map of lattices Lattice theory Module-like...

structure of a lattice Complemented lattice – Bound lattice in which every element has a complement Fréchet lattice – Topological vector lattice Locally convex...

ring Ring theory Lattice-like Lattice Semilattice Complemented lattice Total order Heyting algebra Boolean algebra Map of lattices Lattice theory Module-like...

Folkert; Pallo, Jean Marcel; Stasheff, Jim, eds. (2012), Associahedra, Tamari Lattices and Related Structures: Tamari Memorial Festschrift, Springer, p. 11,...

Bounded lattice: a lattice with a greatest element and least element. Complemented lattice: a bounded lattice with a unary operation, complementation, denoted...

ring Ring theory Lattice-like Lattice Semilattice Complemented lattice Total order Heyting algebra Boolean algebra Map of lattices Lattice theory Module-like...

ring Ring theory Lattice-like Lattice Semilattice Complemented lattice Total order Heyting algebra Boolean algebra Map of lattices Lattice theory Module-like...