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...
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Factorization (redirect from Factorisation)
In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object...
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Fermat's factorization method (redirect from Fermat factorisation)
the square Factorization of polynomials Factor theorem FOIL rule Monoid factorisation Pascal's triangle Prime factor Factorization Euler's factorization...
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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...
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Transformation semigroup Monoid Aperiodic monoid Free monoid Monoid (category theory) Monoid factorisation Syntactic monoid Structure Group (mathematics)...
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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...
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Unique factorization domain (redirect from Unique factorisation)
Algebraic structures Group-like Group Semigroup / Monoid Rack and quandle Quasigroup and loop Abelian group Magma Lie group Group theory Ring-like Ring...
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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...
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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...
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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...
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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...
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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...
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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):...
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