BRAIDS AND THEIR MONOTONE CLONES

被引：10

作者：

DAVEY, BA

NATION, JB

MCKENZIE, RN

PALFRY, PP

机构：

[1] UCB,DEPT MATH,BERKELEY,CA

[2] LA TROBE UNIV,DEPT MATH,BUNDOORA,VIC 3083,AUSTRALIA

[3] UNIV HAWAII,DEPT MATH,HONOLULU,HI 96822

[4] HUNGARIAN ACAD SCI,INST MATH,H-1361 BUDAPEST 5,HUNGARY

来源：

ALGEBRA UNIVERSALIS | 1994年 / 32卷 / 02期

关键词：

D O I：

10.1007/BF01191536

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we investigate properties of the monotone clones of certain ordered sets known as braids. This class of ordered sets arose naturally in the study of how the clone of monotone functions on an ordered set could satisfy, or fail to satisfy, Mal'cev conditions. One version of the main result can be stated as follows. If B is a finite braid with reach r(B) > 2 (defined in the text), then the only idempotent order-preserving functions f: B(n) --> B are the n projections. It then follows, for example, that no algebra of monotone functions on a finite braid B with r(B) > 2 generates a congruence-modular variety.

引用

页码：153 / 176

页数：24