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 commutative monoid M is said to be conical if x+y=0 implies that x=y=0, for any elements x,y of M.
In mathematics, a refinementmonoid 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...
{\displaystyle g\colon M/{\asymp }\to S} such that f=gp. If M is a refinementmonoid, then M / ≍ {\displaystyle M/{\asymp }} is a distributive semilattice...
definition of the free partially commutative monoid or trace monoid, or equivalently, the history monoid, which provides a concrete algebraic foundation...
mathematics and received his doctorate in 1983 with his thesis on refinementmonoids, Vaught monoids and Boolean algebras at the mathematics department at the...
Laboratory.” Trace theory, the general theory of traces. Trace monoid and history monoid Ease programming language XC programming language VerilogCSP is...
(S^{0},S^{1},\dots )} has the structure of a monoid and spectra are just modules over this monoid. If this monoid was commutative, then a monoidal structure...
group Group ring Group with operators Heap Linear algebra Magma Module MonoidMonoid ring Quandle Quasigroup Quantum group Ring Semigroup Vector space Affine...
techniques in the semantics of model theory, most importantly presenting a refinement of canonical model that became standard, and introducing the technique...
for finding the length of the longest increasing subsequence Plactic monoid – monoid of positive integers modulo Knuth equivalencePages displaying wikidata...
called Con X by convention. The canonical map ker : X^X → Con X, relates the monoid X^X of all functions on X and Con X. ker is surjective but not injective...
Tietze The Hauptvermutung, a conjecture on the existence of a common refinement of two triangulations. This was an open problem, for manifolds, to 1961...
arbitrary partial commutative monoid instead of a particular heap model. Later, by suitable choice of commutative monoid, it was surprisingly found that...
ISBN 9783540430674. Meseguer, Jose; Montanari, Ugo (October 1990). "Petri nets are monoids". Information and Computation. 88 (2): 105–155. doi:10.1016/0890-5401(90)90013-8...
they show that the set of exotic spheres of dimension n – specifically the monoid of smooth structures on the standard n-sphere – is isomorphic to the group...
In mathematics, directed algebraic topology is a refinement of algebraic topology for directed spaces, topological spaces and their combinatorial counterparts...
} {\displaystyle X=\{a,b\}} , X ∗ {\displaystyle X^{*}} to be the free monoid generated by X {\displaystyle X} and A {\displaystyle {\mathfrak {A}}} to...
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