Geodesic
Monotonic valuations of $\pi \sigma $-triads and evaluations of ideals
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 1, pp. 23-32.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We develop problems of monotonic valuations of triads. A theorem on monotonic valuations of triads of the type $\pi \sigma $ is presented. We study, using the notion of the monotonic valuation, representations of ideals by monotone and subadditive mappings. We prove, for example, that there exists, for each ideal $J$ of the type $\pi $ on a set $A$, a monotone and subadditive set-mapping $h$ on $P(A)$ with values in non-negative rational numbers such that $J = h^{-1}{''}\{r\in Q;\,r\geq 0 \ r\doteq 0\}$. Some analogical results are proved for ideals of the types $\sigma ,\,\sigma \pi $ and $\pi \sigma $, too. A problem of an additive representation is also discussed.
Classification : 03E70, 20M14, 93A15
Keywords: monotonic valuations; ideal; semigroup 
@article{CMUC_1993__34_1_a2,
     author = {Ml\v{c}ek, Josef},
     title = {Monotonic valuations of $\pi \sigma $-triads and evaluations of ideals},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {23--32},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {1993},
     mrnumber = {1240200},
     zbl = {0792.03034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1993__34_1_a2/}
}
TY  - JOUR
AU  - Mlček, Josef
TI  - Monotonic valuations of $\pi \sigma $-triads and evaluations of ideals
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1993
SP  - 23
EP  - 32
VL  - 34
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_1993__34_1_a2/
LA  - en
ID  - CMUC_1993__34_1_a2
ER  - 
%0 Journal Article
%A Mlček, Josef
%T Monotonic valuations of $\pi \sigma $-triads and evaluations of ideals
%J Commentationes Mathematicae Universitatis Carolinae
%D 1993
%P 23-32
%V 34
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_1993__34_1_a2/
%G en
%F CMUC_1993__34_1_a2
Mlček, Josef. Monotonic valuations of $\pi \sigma $-triads and evaluations of ideals. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 1, pp. 23-32. http://geodesic.mathdoc.fr/item/CMUC_1993__34_1_a2/