Re: Universal algebra with only unary operations

[Cc'ed to poster, since the original was posted some time ago, and I
cannot post to alt.math]

In article <1120165331.629637.260020@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Victor Porton <porton@xxxxxxxxxxx> wrote:
>http://www.mathematics21.org/formulas-theory.html
>^^^
>In this article I have build a (useful) theory of universal algebras
>_with only unary operations_. I have called an universal algebra
>having only unary operations "a basis".

The book by Burris and Sankappanavar simply calls them "unary
algebras". In addition, a finite unary algebra with finitely many
unary operations is called an "automaton".

>Any others' materials about such algebras? Are there any customary
>name for what I call "a basis" (that is universal algebra with only
>unary operations)?

Searching MathSciNet for "unary algebra" in the title gives over 100
hits, though some of them are for mono-unary algebras (algebras which
have only one operation which is unary).

Some titles from a quick perusal of the first 25:

Unary algebras, semigroups and congruences on free semigroups.
Petkovic, Tatjana; Ciric, Miroslav; Bogdanovic, Stojan.
Theoret. Comput. Sci. 324 (2004), no. 1, 87--105. MR 2083930
(2005f:68074)


MR2013740 (2004h:08006)
Bogdanovic, S.; Ciric, M.; Imreh, B.; Petkovic, T.; Steinby, M.
On local properties of unary algebras.
Algebra Colloq. 10 (2003), no. 4, 461--478.


MR1826479 (2002b:08007)
Piro, Konrad(PL-WASW-IM)
On subalgebra lattices of a finite unary algebra. I, II.
Math. Bohem. 126 (2001), no. 1, 161--170, 171--181.


MR1414133 (98c:08007)
Radeleczki, Sandor(H-MIS-IM)
The automorphism group of unary algebras.
Math. Pannon. 7 (1996), no. 2, 253--271.



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Arturo Magidin
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