Two-element Boolean algebra Topics relating to the group theory behind modular arithmetic: Cyclic group Multiplicative group of integers modulo n Other important...

{\displaystyle X,} the measure algebra of ( X , μ ) {\displaystyle (X,\mu )} is the Boolean algebra of all Borel sets modulo μ {\displaystyle \mu } -null...

In algebra, the kernel of a homomorphism is the relation describing how elements in the domain of the homomorphism become related in the image. A homomorphism...

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

In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center...

mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure...

representations of a Lie algebra, using linear algebra. Every connected Lie group is isomorphic to its universal cover modulo a discrete central subgroup...

In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations...

a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n. That is, g is a primitive root modulo n if for every integer...

an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often generalized to polynomials, other expressions...

theory of rings, a branch of abstract algebra, it is described as the group of units of the ring of integers modulo n. Here units refers to elements with...

In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite...

In mathematics, a ring is an algebraic structure consisting of a set with two binary operations called addition and multiplication, which obey the same...

In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more...

In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a...

The ring Z / n Z {\displaystyle \mathbb {Z} /n\mathbb {Z} } of integers modulo n has characteristic n. If R is a subring of S, then R and S have the same...

A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in...

published in 2012:. The Hecke algebra may also be reduced modulo 2. It is defined to be the algebra generated by Hecke operators modulo 2, over F 2 {\displaystyle...

central notions of commutative algebra and homological algebra, and are used widely in algebraic geometry and algebraic topology. In a vector space, the...

Boolean algebra that is both countable and atomless. The complete Cantor algebra is the complete Boolean algebra of Borel subsets of the reals modulo meager...

Lebesgue measurable sets, the Boolean algebra is called the random algebra. The Boolean algebra of all Baire sets modulo meager sets in a topological space...

A non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative...

reducing them modulo one or several prime numbers. For example, the fastest known algorithms for polynomial factorization and linear algebra over the field...

mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of...

enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal...

view of abstract algebra, congruence modulo n {\displaystyle n} is a congruence relation on the ring of integers, and arithmetic modulo n {\displaystyle...

elements. An example is the ring of integers modulo 2. Every Boolean ring gives rise to a Boolean algebra, with ring multiplication corresponding to conjunction...

In set theory, the random algebra or random real algebra is the Boolean algebra of Borel sets of the unit interval modulo the ideal of measure zero sets...

In algebra, a unit or invertible element of a ring is an invertible element for the multiplication of the ring. That is, an element u of a ring R is a...

and isomorphism theorem for more). Two members of a ring or an algebra are congruent modulo an ideal, if the difference between them is in the ideal. Used...