On some non-obvious connections between graphs and unary partial algebras

Title:

On some non-obvious connections between graphs and unary partial algebras

Creator:

Pióro, Konrad

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:5504e9dc-f821-4608-be83-7848a38791c0
uuid:5504e9dc-f821-4608-be83-7848a38791c0

Subject:

math, graphs, and subalgebra lattices of unary partial algebras

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In the present paper we generalize a few algebraic concepts to graphs. Applying this graph language we solve some problems on subalgebra lattices of unary partial algebras. In this paper three such problems are solved, other will be solved in papers [Pió I], [Pió II], [Pió III], [Pió IV]. More precisely, in the present paper first another proof of the following algebraic result from [Bar1] is given: for two unary partial algebras $\mathbf A$ and $\mathbf B$, their weak subalgebra lattices are isomorphic if and only if their graphs ${\mathbf G}^{\ast }({\mathbf A})$ and ${\mathbf G}^{\ast }({\mathbf B})$ are isomorphic. Secondly, it is shown that for two unary partial algebras $\mathbf A$ and $\mathbf B$ if their digraphs ${\mathbf G}({\mathbf A})$ and ${\mathbf G}({\mathbf B})$ are isomorphic, then their (weak, relative, strong) subalgebra lattices are also isomorphic. Thirdly, we characterize pairs $<{\mathbf L},{\mathbf A}>$, where $\mathbf A$ is a unary partial algebra and $\mathbf L$ is a lattice such that the weak subalgebra lattice of $\mathbf A$ is isomorphic to $\mathbf L$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

295-320

Source:

Czechoslovak Mathematical Journal | 2000 Volume:50 | Number:2

Harvested from:

CDK

Metadata only:

false