# On subalgebra lattices of a finite unary algebra. I.

Mathematica Bohemica (2001)

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

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topPióro, 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 -

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