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 ,...

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...

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

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

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

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

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...

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...

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

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...

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

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...

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...

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...

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

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

the same time, semirings are a generalization of bounded distributive lattices. The smallest semiring that is not a ring is the two-element Boolean algebra...

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

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...

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

is an R-subalgebra that is a lattice. In general, there are a lot fewer orders than lattices; e.g., ⁠1/2⁠Z is a lattice in Q but not an order (since it...

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...

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...

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...

abelian group G {\displaystyle G} then A {\displaystyle A} admits a direct complement: a subgroup C {\displaystyle C} of G {\displaystyle G} such that G = A...