<abstract xmlns="http://www.w3.org/1999/xhtml"><p>A generalized hypersubstitution of type τ = (2) is a mapping which maps the binary operation symbol f to a term σ(f) which does not necessarily preserve the arity. Any such σ can be inductively extended to a map σ̂ on the set of all terms of type τ = (2), and any two such extensions can be composed in a natural way. Thus, the set HypG(2) of all generalized hypersubstitutions of type τ = (2) forms a monoid. Green's relations on the monoid of all hypersubstitutions of type τ = (2) were studied by K. Denecke and Sh.L. Wismath. In this paper we describe the classes of generalized hypersubstitutions of type τ = (2) under Green's relations.</p></abstract>

A generalized hypersubstitution of type τ = (2) is a mapping which maps the binary operation symbol f to a term σ(f) which does not necessarily preserve the arity. Any such σ can be inductively extended to a map σ̂ on the set of all terms of type τ = (2), and any two such extensions can be composed in a natural way. Thus, the set HypG(2) of all generalized hypersubstitutions of type τ = (2) forms a monoid. Green's relations on the monoid of all hypersubstitutions of type τ = (2) were studied by K. Denecke and Sh.L. Wismath. In this paper we describe the classes of generalized hypersubstitutions of type τ = (2) under Green's relations.

Green's Relations on Hyp<sub>G</sub>(2)

Department of Mathematics, Materials Science Research Center, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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A generalized hypersubstitution of type τ = (2) is a mapping which maps the binary operation symbol f to a term σ(f) which does not necessarily preserve the...

Green's Relations on Hyp_G(2)

Published Online: May 17, 2013

Page range: 249 - 264

DOI: https://doi.org/10.2478/v10309-012-0016-5

Keywords
Green's relations, Generalized Hypersubstitution

This content is open access.

Green's Relations on HypG(2)