Geodesic
Construction of $po$-groups with quasi-divisors theory
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 1, pp. 197-207 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

A method is presented making it possible to construct $po$-groups with a strong theory of quasi-divisors of finite character and with some prescribed properties as subgroups of restricted Hahn groups $H(\Delta ,\mathbb{Z})$, where $\Delta $ are finitely atomic root systems. Some examples of these constructions are presented.
A method is presented making it possible to construct $po$-groups with a strong theory of quasi-divisors of finite character and with some prescribed properties as subgroups of restricted Hahn groups $H(\Delta ,\mathbb{Z})$, where $\Delta $ are finitely atomic root systems. Some examples of these constructions are presented.
Classification : 06F15, 13F05, 13F99, 13J25
Keywords: quasi-divisor theory; divisor class group 
@article{CMJ_2000_50_1_a20,
     author = {Mo\v{c}ko\v{r}, Ji\v{r}{\'\i}},
     title = {Construction of $po$-groups with quasi-divisors theory},
     journal = {Czechoslovak Mathematical Journal},
     pages = {197--207},
     year = {2000},
     volume = {50},
     number = {1},
     mrnumber = {1745472},
     zbl = {1036.06009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2000_50_1_a20/}
}
TY  - JOUR
AU  - Močkoř, Jiří
TI  - Construction of $po$-groups with quasi-divisors theory
JO  - Czechoslovak Mathematical Journal
PY  - 2000
SP  - 197
EP  - 207
VL  - 50
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2000_50_1_a20/
LA  - en
ID  - CMJ_2000_50_1_a20
ER  - 
%0 Journal Article
%A Močkoř, Jiří
%T Construction of $po$-groups with quasi-divisors theory
%J Czechoslovak Mathematical Journal
%D 2000
%P 197-207
%V 50
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2000_50_1_a20/
%G en
%F CMJ_2000_50_1_a20
Močkoř, Jiří. Construction of $po$-groups with quasi-divisors theory. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 1, pp. 197-207. http://geodesic.mathdoc.fr/item/CMJ_2000_50_1_a20/

[1] Anderson, M., Feil, T.: Lattice-ordered Groups. D. Reidl Publ. Co., Dordrecht, Tokyo, 1988. | MR

[2] Aubert, K.E.: Divisors of finite character. Annali di matem. pura ed appl. 33 (1983), 327–361. | MR | Zbl

[3] Aubert, K.E.: Localizations dans les systémes d’idéaux. C.R.Acad. Sci. Paris 272 (1971), 465–468. | MR

[4] Borevich, Z. I. and Shafarevich, I. R.: Number Theory. Academic Press, New York, 1966. | MR

[5] Conrad, P.: Lattice Ordered Groups. Tulane University, 1970. | Zbl

[6] Chouinard, L. G.: Krull semigroups and divisor class group. Canad. J. Math. 33 (1981), 1459–1468. | DOI | MR

[7] Geroldinger, A., Močkoř, J.: Quasi-divisor theories and generalizations of Krull domains. J. Pure Appl. Algebra 102 (1995), 289–311. | DOI | MR

[8] Gilmer, R.: Multiplicative Ideal Theory. M. Dekker, Inc., New York, 1972. | MR | Zbl

[9] Griffin, M.: Rings of Krull type. J. Reine Angew. Math. 229 (1968), 1–27. | MR | Zbl

[10] Griffin, M.: Some results on v-multiplication rings. Canad. J. Math. 19 (1967), 710–722. | DOI | MR | Zbl

[11] Jaffard, P.: Les systémes d’idéaux. Dunod, Paris, 1960. | MR | Zbl

[12] Močkoř, J.: Groups of Divisibility. D. Reidl Publ. Co., Dordrecht, 1983. | MR

[13] Močkoř, J., Alajbegovic, J.: Approximation Theorems in Commutative Algebra. Kluwer Academic publ., Dordrecht, 1992. | MR

[14] Močkoř, J.,Kontolatou, A.: Groups with quasi-divisor theory. Comm. Math. Univ. St. Pauli, Tokyo 42 (1993), 23–36. | MR

[15] Močkoř, J.,Kontolatou, A.: Divisor class groups of ordered subgroups. Acta Math. Inform. Univ. Ostraviensis 1 (1993). | MR

[16] Močkoř, J., Kontolatou, A.: Quasi-divisors theory of partly ordered groups. Grazer Math. Ber. 318 (1992), 81–98. | MR

[17] Močkoř, J.: $t$-Valuation and theory of quasi-divisors. To appear in J. Pure Appl. Algebra. | MR

[18] Močkoř, J., Kontolatou, A.: Some remarks on Lorezen $r$-group of partly ordered group. Czechoslovak Math. J. 46(121) (1996), 537–552. | MR

[19] Močkoř, J.: Divisor class group and the theory of quasi-divisors. To appear. | MR

[20] Ohm, J.: Semi-valuations and groups of divisibility. Canad. J. Math. 21 (1969), 576–591. | DOI | MR | Zbl

[21] Skula, L.: Divisorentheorie einer Halbgruppe. Math. Z. 114 (1970), 113–120. | MR | Zbl

[22] Skula, L.: On $c$-semigroups. Acta Arith. 31 (1976), 247–257. | DOI | MR | Zbl