mathematics, a factorisation of a free monoid is a sequence of subsets of words with the property that every word in the free monoid can be written as...

In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object...

the square Factorization of polynomials Factor theorem FOIL rule Monoid factorisation Pascal's triangle Prime factor Factorization Euler's factorization...

provide a unique monoid factorisation of the free monoid. They are also totally ordered, and thus provide a total order on the monoid. This is analogous...

Transformation semigroup Monoid Aperiodic monoid Free monoid Monoid (category theory) Monoid factorisation Syntactic monoid Structure Group (mathematics)...

variables with coefficients in the ring R is the monoid ring R[N], where the monoid N is the free monoid on n letters, also known as the set of all strings...

Algebraic structures Group-like Group Semigroup / Monoid Rack and quandle Quasigroup and loop Abelian group Magma Lie group Group theory Ring-like Ring...

greater than m, and the ni are integers. Hall–Petresco identity Monoid factorisation Hall, Philip (1934), "A contribution to the theory of groups of prime-power...

to complete proofs in the general case of Fermat's Last Theorem by factorisation using the roots of unity was for a very good reason: a failure of unique...

countably infinite) P of G, such that every element a ≠ 1 in G has a unique factorisation of the form a = p 1 α 1 p 2 α 2 ⋯ p r α r {\displaystyle a=p_{1}^{\alpha...

exist, their objects are isomorphic. Put more precisely, we have a factorisation of f: A → B as A → C → I → B, where the morphism on the left is the...

strings contain one. Formally, let A be an alphabet and A∗ be the free monoid of finite strings over A. Every non-empty word w in A+ is a sesquipower...

1016/0022-247X(63)90070-2, MR 0158002. Schützenberger, M. P. (1965), "On a factorisation of free monoids", Proceedings of the American Mathematical Society, 16 (1):...