Refinement monoids and adaptable separated graphs | Zendy

Pere Ara | Zendy; Joan Bosa | Zendy; Enrique Pardo | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Refinement monoids and adaptable separated graphs

Author(s) -

Pere Ara,

Joan Bosa,

Enrique Pardo

Publication year - 2019

Publication title -

semigroup forum

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.52

H-Index - 38

eISSN - 1432-2137

pISSN - 0037-1912

DOI - 10.1007/s00233-019-10077-2

Subject(s) - monoid , mathematics , syntactic monoid , von neumann architecture , free monoid , conical surface , subclass , graph , combinatorics , realization (probability) , algebra over a field , discrete mathematics , pure mathematics , statistics , geometry , antibody , immunology , biology

We define a subclass of separated graphs, the class of adaptable separated graphs, and study their associated monoids. We show that these monoids are primely generated conical refinement monoids, and we explicitly determine their associated I-systems. We also show that any finitely generated conical refinement monoid can be represented as the monoid of an adaptable separated graph. These results provide the first step toward an affirmative answer to the Realization Problem for von Neumann regular rings, in the finitely generated case.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research