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Qu'est-ce (qui) est quasi-integral lattice-ordered semigroup - définition

PARTIALLY ORDERED VECTOR SPACE, ORDERED AS A LATTICE

Lattice-ordered vector space; Vector lattice

Riesz space

In mathematics, a Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice.

https://en.wikipedia.org/wiki/Riesz_space

Monogenic semigroup

SEMIGROUP GENERATED BY A SINGLE ELEMENT

Cyclic semigroup; Periodic semigroup

In mathematics, a monogenic semigroup is a semigroup generated by a single element. Monogenic semigroups are also called cyclic semigroups.

https://en.wikipedia.org/wiki/Monogenic_semigroup

Well-quasi-ordering

$'''Pic.3:''' Hasse diagram of <math>\N^2</math> with componentwise order$

PREORDER IN WHICH EVERY INFINITE SEQUENCE HAS AN INCREASING OR EQUIVALENT PAIR OF CONSECUTIVE VALUES

Well partial order; WQO; Well quasi ordering; Wellquasiorder; Well-quasi-order; Well quasi order; Wqo; Well-quasi order; Well-partial-order

In mathematics, specifically order theory, a well-quasi-ordering or wqo is a quasi-ordering such that any infinite sequence of elements x_0, x_1, x_2, \ldots from X contains an increasing pair x_i\le x_j with i.

https://en.wikipedia.org/wiki/Well-quasi-ordering

Wikipédia

Riesz space

In mathematics, a Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice.

Riesz spaces are named after Frigyes Riesz who first defined them in his 1928 paper Sur la décomposition des opérations fonctionelles linéaires.

Riesz spaces have wide-ranging applications. They are important in measure theory, in that important results are special cases of results for Riesz spaces. For example, the Radon–Nikodym theorem follows as a special case of the Freudenthal spectral theorem. Riesz spaces have also seen application in mathematical economics through the work of Greek-American economist and mathematician Charalambos D. Aliprantis.

https://en.wikipedia.org/wiki/Riesz space