mathematics, a Boolean ring R is a ring for which x2 = x for all x in R, that is, a ring that consists of only idempotent elements. An example is the ring of integers...

Every Boolean algebra gives rise to a Boolean ring, and vice versa, with ring multiplication corresponding to conjunction or meet ∧, and ring addition...

of Boolean variables whose state is determined by other variables in the network Boolean processor, a 1-bit variable computing unit Boolean ring, a mathematical...

of a ring Simplicial commutative ring Special types of rings: Boolean ring Dedekind ring Differential ring Exponential ring Finite ring Lie ring Local...

any set becomes a Boolean ring, with symmetric difference as the addition of the ring and intersection as the multiplication of the ring. The symmetric difference...

connected to homological properties of the ring. In Boolean algebra, the main objects of study are rings in which all elements are idempotent under both...

distributive lattices. The smallest semiring that is not a ring is the two-element Boolean algebra, for instance with logical disjunction ∨ {\displaystyle...

In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the...

operations on a set Two-element Boolean algebra, Boolean algebra whose underlying set has two elements Boolean ring Boolean (disambiguation) This disambiguation...

In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY...

such as complex numbers, polynomials, matrices, rings, and fields. It is also encountered in Boolean algebra and mathematical logic, where each of the...

elements, so any module over a Boolean ring is locally free, but there are some non-projective modules over Boolean rings. One example is R/I where R is...

Boolean algebras are models of the equational theory of two values; this definition is equivalent to the lattice and ring definitions. Boolean algebra...

algebras is isomorphic to the category of Boolean rings. Given a Boolean algebra B, we turn B into a Boolean ring by using the symmetric difference as addition...

Algorithmic information theory Boolean ring commutativity of a boolean ring Boolean satisfiability problem NP-completeness of the Boolean satisfiability problem...

power set considered together with both of these operations forms a Boolean ring. In set theory, XY is the notation representing the set of all functions...

\alpha _{2}\in \mathbb {C} \}} . The prime spectrum of a Boolean ring (e.g., a power set ring) is a compact totally disconnected Hausdorff space (that...

over fields or rings in ring theory. Fields of sets play an essential role in the representation theory of Boolean algebras. Every Boolean algebra can be...

of Boolean variables whose state is determined by other variables in the network Boolean processor, a 1-bit variables computing unit Boolean ring, a ring...

a system of non-linear modular arithmetic equations is NP-complete. Boolean ring Circular buffer Division (mathematics) Finite field Legendre symbol Modular...

every r, the ring is called Boolean ring. More general conditions which guarantee commutativity of a ring are also known. A graded ring R = ⨁i∊Z Ri is...

is set inclusion. Also, they are exactly ideals in the ring-theoretic sense on the Boolean ring formed by the powerset of the underlying set. The dual...

square (every element is idempotent) is called a Boolean ring; an example from computer science is the ring whose elements are binary numbers, with bitwise...

Neumann regular rings. The ring of affiliated operators of a finite von Neumann algebra is von Neumann regular. A Boolean ring is a ring in which every...

In mathematics, Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a certain field of sets. The theorem...

LCM are idempotent. In a Boolean ring, multiplication is idempotent. In a Tropical semiring, addition is idempotent. In a ring of quadratic matrices, the...

example, the inverse of 3 modulo 11 is 8, as 3 + 8 ≡ 0 (mod 11). In a Boolean ring, which has elements { 0 , 1 } {\displaystyle \{0,1\}} addition is often...

In mathematics, a Noetherian ring is a ring that satisfies the ascending chain condition on left and right ideals; if the chain condition is satisfied...

(with involution) Łukasiewicz–Moisil algebra Boolean algebra (structure) Boolean ring Complete Boolean algebra Orthocomplemented lattice Quantale Partially...

In mathematics, the Boolean prime ideal theorem states that ideals in a Boolean algebra can be extended to prime ideals. A variation of this statement...