Garside monoids vs divisibility monoids | Mathematical...

来自 : www.onacademic.com/detail/jour 发布时间：2021-03-25

Author: PICANTIN MATTHIEU

Journal: Mathematical Structures in Computer Science

Issue Date: 2005

Abstract(summary):
Divisibility monoids are a natural algebraic generalisation of Mazurkiewicz trace monoids, namely monoids in which the distributivity of the underlying lattices is kept as a hypothesis, but the relations between the generators are not necessarily supposed to be commutations. Garside monoids are a natural algebraic generalisation of spherical Artin monoids, namely monoids in which the existence of common multiples is kept as a hypothesis, but the relations between the generators are not necessarily supposed to be of Coxeter type. Here, we show that the quasi-centre of these monoids can be studied and described in a similar way, and then we exhibit the intersection between the two classes of monoids

Page: 231-242


Garside monoids are a natural algebraic generalisation of spherical Artin monoids, namely monoids in which the existence of common multiples is kept as ...onAcademic ；Science；Technology；Medicine；researchDivisibility monoids are a natural algebraic generalisation of Mazurkiewicz trace monoids, namely monoids in which the distributivity of the underlying lattices is kept as a hypothesis, but the relations between the generators are not necessarily supposed to be commutations. Garside monoids are a natural algebraic generalisation of spherical Artin monoids, namely monoids in which the existence of common multiples is kept as a hypothesis, but the relations between the generators are not necessarily supposed to be of Coxeter type. Here, we show that the quasi-centre of these monoids can be studied and described in a similar way, and then we exhibit the intersection between the two classes of monoidsGarside monoids vs divisibility monoids