Identities in Graph Algebras of Type (n, n − 1, ..., 3, 2, 0)

T. Poomsa-ard, J. Wetweerapong, C. Khiloukom, T. Musuntei

Abstract


Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity $s \thickapprox t $ if the corresponding graph algebra A(G) satisfies $s \thickapprox t.$ In this paper we generalize the concept of graph algebras of type $\tau = (2, 0)$ to define graph algebras of type $\tau = (n, n−1, n−2, ..., 3, 2, 0), n \geqslant 2$ and characterize identities in graph algebras. Further we show that any term over the class of all graph algebras can be uniquely represented by a normal form term and that there is an algorithm to construct the normal form term to every given term t.

Full Text: PDF

Refbacks

  • There are currently no refbacks.


The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

Copyright 2020 by the Mathematical Association of Thailand.

All rights reserve. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission of the Mathematical Association of Thailand.

|ISSN 1686-0209|