Varieties of algebras arising from K-perfect m-cycle systems

Brier, R and Bryant, D (2006) Varieties of algebras arising from K-perfect m-cycle systems. Discrete Mathematics, 306 17: 2038-2046. doi:10.1016/j.disc.2006.04.002


Author Brier, R
Bryant, D
Title Varieties of algebras arising from K-perfect m-cycle systems
Journal name Discrete Mathematics   Check publisher's open access policy
ISSN 0012-365X
Publication date 2006-01-01
Sub-type Article (original research)
DOI 10.1016/j.disc.2006.04.002
Volume 306
Issue 17
Start page 2038
End page 2046
Total pages 9
Editor Peter L Hammer
Place of publication Amsterdam
Publisher Elsevier Science Bv
Language eng
Subject C1
230101 Mathematical Logic, Set Theory, Lattices And Combinatorics
230103 Rings And Algebras
780101 Mathematical sciences
Abstract A class of algebras forms a variety if it is characterised by a collection of identities. There is a well-known method, often called the standard construction, which gives rise to algebras from m-cycle systems. It is known that the algebras arising from {1}-perfect m-cycle systems form a variety for m is an element of {3, 5} only, and that the algebras arising from {1, 2}-perfect m-cycle systems form a variety for m is an element of {3, 5, 7} only. Here we give, for any set K of positive integers, necessary and sufficient conditions under which the algebras arising from K-perfect m-cycle systems form a variety. (c) 2006 Elsevier B.V. All rights reserved.
Keyword Homomorphism
K-perfect M-cycle System
M-circuit System
Variety
Mathematics
M=3
Q-Index Code C1

 
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Created: Wed, 15 Aug 2007, 19:28:04 EST