free monoid
Смотреть что такое "free monoid" в других словарях:
Free monoid — In abstract algebra, the free monoid on a set A is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from A , with the binary operation of concatenation. It is usually denoted A lowast;. The identity… … Wikipedia
Monoid — This article is about the mathematical concept. For the alien creatures in the Doctor Who adventure, see The Ark (Doctor Who). Coherence law for monoid unit In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a… … Wikipedia
Free object — In mathematics, the idea of a free object is one of the basic concepts of abstract algebra. It is a part of universal algebra, in the sense that it relates to all types of algebraic structure (with finitary operations). It also has a clean… … Wikipedia
Free algebra — This article is about free algebras in ring theory. For the more general free algebras in universal algebra, see free object. In mathematics, especially in the area of abstract algebra known as ring theory, a free algebra is the noncommutative… … Wikipedia
Monoid ring — In abstract algebra, a monoid ring is a new ring constructed from some other ring and a monoid. Definition Let R be a ring and G be a monoid. Consider all the functions φ : G → R such that the set {g: φ(g) ≠ 0} is finite. Let all such… … Wikipedia
Free group — In mathematics, a group G is called free if there is a subset S of G such that any element of G can be written in one and only one way as a product of finitely many elements of S and their inverses (disregarding trivial variations such as st 1 =… … Wikipedia
Presentation of a monoid — In algebra, a presentation of a monoid (or semigroup) is a description of a monoid (or semigroup) in terms of a set Sigma; of generators and a set of relations on the free monoid Sigma; lowast; (or free semigroup Sigma;+) generated by Sigma;. The … Wikipedia
History monoid — In mathematics and computer science, a history monoid is a way of representing the histories of concurrently running computer processes as a collection of strings, each string representing the individual history of a process. The history monoid… … Wikipedia
Trace monoid — In mathematics and computer science, a trace is a set of strings, wherein certain letters in the string are allowed to commute, but others are not. It generalizes the concept of a string, by not forcing the letters to always be in a fixed order,… … Wikipedia
Refinement monoid — In mathematics, a refinement monoid is a commutative monoid M such that for any elements a0, a1, b0, b1 of M such that a0+a1=b0+b1, there are elements c00, c01, c10, c11 of M such that a0=c00+c01, a1=c10+c11, b0=c00+c10, and b1=c01+c11. A… … Wikipedia
Aperiodic monoid — In mathematics, an aperiodic semigroup is a semigroup S such that for every x ∈ S , there exists a nonnegative integer n such that xn = xn + 1 .An aperiodic monoid is an aperiodic semigroup which is a monoid. This notion is in some sense… … Wikipedia
