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- Title
Tame and wild refinement monoids.
- Authors
Ara, P.; Goodearl, K.
- Abstract
The class of refinement monoids (commutative monoids satisfying the Riesz refinement property) is subdivided into those which are tame, defined as being an inductive limit of finitely generated refinement monoids, and those which are wild, i.e., not tame. It is shown that tame refinement monoids enjoy many positive properties, including separative cancellation ( $$2x=2y=x+y \implies x=y$$ ) and multiplicative cancellation with respect to the algebraic ordering ( $$mx\le my \implies x\le y$$ ). In contrast, examples are constructed to exhibit refinement monoids which enjoy all the mentioned good properties but are nonetheless wild.
- Subjects
TAME algebras; MONOIDS; SET theory; COMMUTATIVE algebra; FINITE groups
- Publication
Semigroup Forum, 2015, Vol 91, Issue 1, p1
- ISSN
0037-1912
- Publication type
Article
- DOI
10.1007/s00233-014-9647-3