Definition & Betydelse | Engelska ordet SEMIGROUP

Definition av SEMIGROUP

1. (matematik) semigrupp

Exempel på hur man kan använda SEMIGROUP i en mening

• In mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix.
• In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it.
• Nevertheless, influential books in semigroup theory, including Clifford and Preston (1961) and Howie (1995) use groupoid in the sense of Hausmann and Ore.
• The idealizer in a semigroup or ring is another construction that is in the same vein as the centralizer and normalizer.
• In the symmetric semigroup (of all transformations) one also finds a weaker, non-unique notion of inverse (called a pseudoinverse) because the symmetric semigroup is a regular semigroup.
• On the other hand, if the non-zero entries are only required to be non-zero, but not necessarily invertible, this set of matrices forms a semigroup instead.
• The most important semigroups are, respectively, the heat semigroup, Riemann-Liouville semigroup, and Brownian motion and other infinitely divisible processes.
• In algebra, the bicommutant of a subset S of a semigroup (such as an algebra or a group) is the commutant of the commutant of that subset.
• In a semigroup, a left-invertible element is left-cancellative, and analogously for right and two-sided.
• The Krohn–Rhodes theorem for finite semigroups states that every finite semigroup S is a divisor of a finite alternating wreath product of finite simple groups, each a divisor of S, and finite aperiodic semigroups (which contain no nontrivial subgroups).
• It follows that every monoid (or semigroup) arises as a homomorphic image of a free monoid (or semigroup).
• A finite semigroup is aperiodic if and only if it contains no nontrivial subgroups, so a synonym used (only?) in such contexts is group-free semigroup.
• Notice that although every group becomes a semigroup when the identity as a constant is omitted (and/or the inverse operation is omitted), the class of groups does not form a subvariety of the variety of semigroups because the signatures are different.
• In mathematics, the bicyclic semigroup is an algebraic object important for the structure theory of semigroups.
• Partial isometries (and projections) can be defined in the more abstract setting of a semigroup with involution; the definition coincides with the one herein.
• Considering subgroups, and in particular maximal subgroups, of semigroups often allows one to apply group-theoretic techniques in semigroup theory.
• Every element of S has at least one inverse (S is a regular semigroup) and idempotents commute (that is, the idempotents of S form a semilattice).
• While it is common to use the term transformation for any function of a set into itself (especially in terms like "transformation semigroup" and similar), there exists an alternative form of terminological convention in which the term "transformation" is reserved only for bijections.
• The unary operation that maps a relation to the converse relation is an involution, so it induces the structure of a semigroup with involution on the binary relations on a set, or, more generally, induces a dagger category on the category of relations as detailed below.
• The idempotents of a rectangular semigroup form a sub band that is a rectangular band but a rectangular semigroup may have elements that are not idempotent.

Förberedelsen av sidan tog: 528,48 ms.