A note on normal varieties of monounary algebras

Chajda, Ivan, and Länger, Helmut. "A note on normal varieties of monounary algebras." Czechoslovak Mathematical Journal 52.2 (2002): 369-373. <http://eudml.org/doc/30707>.

@article{Chajda2002,
abstract = {A variety is called normal if no laws of the form $s=t$ are valid in it where $s$ is a variable and $t$ is not a variable. Let $L$ denote the lattice of all varieties of monounary algebras $(A,f)$ and let $V$ be a non-trivial non-normal element of $L$. Then $V$ is of the form $\{\mathrm \{M\}od\}(f^n(x)=x)$ with some $n>0$. It is shown that the smallest normal variety containing $V$ is contained in $\{\mathrm \{H\}SC\}(\{\mathrm \{M\}od\}(f^\{mn\}(x)=x))$ for every $m>1$ where $\{\mathrm \{C\}\}$ denotes the operator of forming choice algebras. Moreover, it is proved that the sublattice of $L$ consisting of all normal elements of $L$ is isomorphic to $L$.},
author = {Chajda, Ivan, Länger, Helmut},
journal = {Czechoslovak Mathematical Journal},
keywords = {monounary algebra; variety; normal variety; choice algebra; monounary algebra; variety; normal variety; choice algebra},
language = {eng},
number = {2},
pages = {369-373},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on normal varieties of monounary algebras},
url = {http://eudml.org/doc/30707},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Chajda, Ivan
AU - Länger, Helmut
TI - A note on normal varieties of monounary algebras
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 2
SP - 369
EP - 373
AB - A variety is called normal if no laws of the form $s=t$ are valid in it where $s$ is a variable and $t$ is not a variable. Let $L$ denote the lattice of all varieties of monounary algebras $(A,f)$ and let $V$ be a non-trivial non-normal element of $L$. Then $V$ is of the form ${\mathrm {M}od}(f^n(x)=x)$ with some $n>0$. It is shown that the smallest normal variety containing $V$ is contained in ${\mathrm {H}SC}({\mathrm {M}od}(f^{mn}(x)=x))$ for every $m>1$ where ${\mathrm {C}}$ denotes the operator of forming choice algebras. Moreover, it is proved that the sublattice of $L$ consisting of all normal elements of $L$ is isomorphic to $L$.
LA - eng
KW - monounary algebra; variety; normal variety; choice algebra; monounary algebra; variety; normal variety; choice algebra
UR - http://eudml.org/doc/30707
ER -