On subalgebra lattices of a finite unary algebra. I.

Konrad Pióro

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 1, page 161-170
  • ISSN: 0862-7959

Abstract

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One of the main aims of the present and the next part [15] is to show that the theory of graphs (its language and results) can be very useful in algebraic investigations. We characterize, in terms of isomorphisms of some digraphs, all pairs 𝐀 , 𝐋 , where 𝐀 is a finite unary algebra and L a finite lattice such that the subalgebra lattice of 𝐀 is isomorphic to 𝐋 . Moreover, we find necessary and sufficient conditions for two arbitrary finite unary algebras to have isomorphic subalgebra lattices. We solve these two problems in the more general case of partial unary algebras. In the next part [15] we will use these results to describe connections between various kinds of lattices of (partial) subalgebras of a finite unary algebra.

How to cite

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Pióro, Konrad. "On subalgebra lattices of a finite unary algebra. I.." Mathematica Bohemica 126.1 (2001): 161-170. <http://eudml.org/doc/248834>.

@article{Pióro2001,
abstract = {One of the main aims of the present and the next part [15] is to show that the theory of graphs (its language and results) can be very useful in algebraic investigations. We characterize, in terms of isomorphisms of some digraphs, all pairs $\langle \mathbf \{A\},\mathbf \{L\}\rangle $, where $\mathbf \{A\}$ is a finite unary algebra and $L$ a finite lattice such that the subalgebra lattice of $\mathbf \{A\}$ is isomorphic to $\mathbf \{L\}$. Moreover, we find necessary and sufficient conditions for two arbitrary finite unary algebras to have isomorphic subalgebra lattices. We solve these two problems in the more general case of partial unary algebras. In the next part [15] we will use these results to describe connections between various kinds of lattices of (partial) subalgebras of a finite unary algebra.},
author = {Pióro, Konrad},
journal = {Mathematica Bohemica},
keywords = {unary algebra; partial algebra; subalgebra lattice; directed graph; finite unary algebra; partial algebra; subalgebra lattice; directed graph},
language = {eng},
number = {1},
pages = {161-170},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On subalgebra lattices of a finite unary algebra. I.},
url = {http://eudml.org/doc/248834},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Pióro, Konrad
TI - On subalgebra lattices of a finite unary algebra. I.
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 1
SP - 161
EP - 170
AB - One of the main aims of the present and the next part [15] is to show that the theory of graphs (its language and results) can be very useful in algebraic investigations. We characterize, in terms of isomorphisms of some digraphs, all pairs $\langle \mathbf {A},\mathbf {L}\rangle $, where $\mathbf {A}$ is a finite unary algebra and $L$ a finite lattice such that the subalgebra lattice of $\mathbf {A}$ is isomorphic to $\mathbf {L}$. Moreover, we find necessary and sufficient conditions for two arbitrary finite unary algebras to have isomorphic subalgebra lattices. We solve these two problems in the more general case of partial unary algebras. In the next part [15] we will use these results to describe connections between various kinds of lattices of (partial) subalgebras of a finite unary algebra.
LA - eng
KW - unary algebra; partial algebra; subalgebra lattice; directed graph; finite unary algebra; partial algebra; subalgebra lattice; directed graph
UR - http://eudml.org/doc/248834
ER -

References

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