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

Mathematica Bohemica (2001)

- Volume: 126, Issue: 1, page 171-181
- ISSN: 0862-7959

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topPióro, Konrad. "On subalgebra lattices of a finite unary algebra. II.." Mathematica Bohemica 126.1 (2001): 171-181. <http://eudml.org/doc/248842>.

@article{Pióro2001,

abstract = {We use graph-algebraic results proved in [8] and some results of the graph theory to characterize all pairs $\langle \mathbf \{L\}_\{1\},\mathbf \{L\}_\{2\}\rangle $ of lattices for which there is a finite partial unary algebra such that its weak and strong subalgebra lattices are isomorphic to $\mathbf \{L\}_\{1\}$ and $\mathbf \{L\}_\{2\}$, respectively. Next, we describe other pairs of subalgebra lattices (weak and relative, etc.) of a finite unary algebra. Finally, necessary and sufficient conditions are found for quadruples $\langle \mathbf \{L\}_\{1\},\mathbf \{L\}_\{2\}, \mathbf \{L\}_\{3\},\mathbf \{L\}_\{4\}\rangle $ of lattices for which there is a finite unary algebra having its weak, relative, strong subalgebra and initial segment lattices isomorphic to $\mathbf \{L\}_\{1\},\mathbf \{L\}_\{2\}, \mathbf \{L\}_\{3\},\mathbf \{L\}_\{4\}$, respectively.},

author = {Pióro, Konrad},

journal = {Mathematica Bohemica},

keywords = {graph; finite unary algebra; partial algebra; subalgebras; subalgebra lattices; graph; finite unary algebra; partial algebra; subalgebras; subalgebra lattices},

language = {eng},

number = {1},

pages = {171-181},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On subalgebra lattices of a finite unary algebra. II.},

url = {http://eudml.org/doc/248842},

volume = {126},

year = {2001},

}

TY - JOUR

AU - Pióro, Konrad

TI - On subalgebra lattices of a finite unary algebra. II.

JO - Mathematica Bohemica

PY - 2001

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 126

IS - 1

SP - 171

EP - 181

AB - We use graph-algebraic results proved in [8] and some results of the graph theory to characterize all pairs $\langle \mathbf {L}_{1},\mathbf {L}_{2}\rangle $ of lattices for which there is a finite partial unary algebra such that its weak and strong subalgebra lattices are isomorphic to $\mathbf {L}_{1}$ and $\mathbf {L}_{2}$, respectively. Next, we describe other pairs of subalgebra lattices (weak and relative, etc.) of a finite unary algebra. Finally, necessary and sufficient conditions are found for quadruples $\langle \mathbf {L}_{1},\mathbf {L}_{2}, \mathbf {L}_{3},\mathbf {L}_{4}\rangle $ of lattices for which there is a finite unary algebra having its weak, relative, strong subalgebra and initial segment lattices isomorphic to $\mathbf {L}_{1},\mathbf {L}_{2}, \mathbf {L}_{3},\mathbf {L}_{4}$, respectively.

LA - eng

KW - graph; finite unary algebra; partial algebra; subalgebras; subalgebra lattices; graph; finite unary algebra; partial algebra; subalgebras; subalgebra lattices

UR - http://eudml.org/doc/248842

ER -

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- On subalgebra lattices of a finite unary algebra, part I, Math. Bohem. 126 (2001), 161–170. (2001) MR1826479
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