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Special m-hyperidentities in biregular leftmost graph varieties of type (2,0)

Apinant Anantpinitwatna, Tiang Poomsa-ard (2009)

Discussiones Mathematicae - General Algebra and Applications

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 a term equation s ≈ t if the corresponding graph algebra A ( G ) ̲ satisfies s ≈ t. A class of graph algebras V is called a graph variety if V = M o d g Σ where Σ is a subset of T(X) × T(X). A graph variety V ' = M o d g Σ ' is called a biregular leftmost graph variety if Σ’ is a set of biregular leftmost term equations. A term equation s ≈ t is called an identity in a variety...

The positive and generalized discriminators don't exist

A.G. Pinus (2000)

Discussiones Mathematicae - General Algebra and Applications

In this paper it is proved that there does not exist a function for the language of positive and generalized conditional terms that behaves the same as the discriminator for the language of conditional terms.

The weak extension property and finite axiomatizability for quasivarieties

Wiesław Dziobiak, Miklós Maróti, Ralph McKenzie, Anvar Nurakunov (2009)

Fundamenta Mathematicae

We define and compare a selection of congruence properties of quasivarieties, including the relative congruence meet semi-distributivity, RSD(∧), and the weak extension property, WEP. We prove that if 𝒦 ⊆ ℒ ⊆ ℒ' are quasivarieties of finite signature, and ℒ' is finitely generated while 𝒦 ⊨ WEP, then 𝒦 is finitely axiomatizable relative to ℒ. We prove for any quasivariety 𝒦 that 𝒦 ⊨ RSD(∧) iff 𝒦 has pseudo-complemented congruence lattices and 𝒦 ⊨ WEP. Applying these results and other results...

T-Varieties and Clones of T-terms

Klaus Denecke, Prakit Jampachon (2005)

Discussiones Mathematicae - General Algebra and Applications

The aim of this paper is to describe how varieties of algebras of type τ can be classified by using the form of the terms which build the (defining) identities of the variety. There are several possibilities to do so. In [3], [19], [15] normal identities were considered, i.e. identities which have the form x ≈ x or s ≈ t, where s and t contain at least one operation symbol. This was generalized in [14] to k-normal identities and in [4] to P-compatible identities. More generally, we select a subset...

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