On invariants related to non-unique factorizations in block monoids and rings of algebraic integers
Mathematica slovaca, Tome 55 (2005) no. 1, pp. 21-37
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 11N64, 11R27, 20D60, 20K01
@article{MASLO_2005_55_1_a2,
     author = {Schmid, Wolfgang A.},
     title = {On invariants related to non-unique factorizations in block monoids and rings of algebraic integers},
     journal = {Mathematica slovaca},
     pages = {21--37},
     year = {2005},
     volume = {55},
     number = {1},
     mrnumber = {2178533},
     zbl = {1108.11074},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MASLO_2005_55_1_a2/}
}
TY  - JOUR
AU  - Schmid, Wolfgang A.
TI  - On invariants related to non-unique factorizations in block monoids and rings of algebraic integers
JO  - Mathematica slovaca
PY  - 2005
SP  - 21
EP  - 37
VL  - 55
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MASLO_2005_55_1_a2/
LA  - en
ID  - MASLO_2005_55_1_a2
ER  - 
%0 Journal Article
%A Schmid, Wolfgang A.
%T On invariants related to non-unique factorizations in block monoids and rings of algebraic integers
%J Mathematica slovaca
%D 2005
%P 21-37
%V 55
%N 1
%U http://geodesic.mathdoc.fr/item/MASLO_2005_55_1_a2/
%G en
%F MASLO_2005_55_1_a2
Schmid, Wolfgang A. On invariants related to non-unique factorizations in block monoids and rings of algebraic integers. Mathematica slovaca, Tome 55 (2005) no. 1, pp. 21-37. http://geodesic.mathdoc.fr/item/MASLO_2005_55_1_a2/

[1] CHAPMAN S. T.-FREEZE M.-GAO W. D.-SMITH W. W.: On Davenport's constant of finite abelian groups. Far East J. Math. Sci. (FJMS) 5 (2002), 47-54. | MR | Zbl

[2] Arithmetical Properties of Commutative Rings and Monoids. (S. T. Chapman, ed.), Lecture Notes in Pure and Appl. Math. 241, Dekker/CRC Press, New York, 2005. | MR | Zbl

[3] GAO W. D.: On Davenport's constant of finite abelian groups with rank three. Discrete Math. 222 (2000), 111-124. | MR | Zbl

[4] GAO W. D.: On a combinatorial problem connected with factorizations. Colloq. Math. 72 (1997), 251-268. | MR | Zbl

[5] GEROLDINGER A.: Ein quantitatives Resultat über Faktorisierungen verschiedener Länge in algebraischen Zahlkörpern. Math. Z. 205 (1990), 159-162. | MR | Zbl

[6] GEROLDINGER A.-HALTER-KOCH F.: Nonunique factorizations in block semigroups and arithmetical applications. Math. Slovaca 42 (1992), 641-661. | MR

[7] GEROLDINGER A.-HALTER-KOCH F.: Congruence monoids. Acta Arith. 112 (2004), 263-296. | MR | Zbl

[8] GEROLDINGER A.-HALTER-KOCH F.: Transfer principles in the theory of non-unique factorization. In: Arithmetical Properties of Commutative Rings and Monoids (S. T. Chapman, ed.), Lecture Notes in Pure and Appl. Math. 241, Dekker/CRC Press, New York, 2005, pp. 114-142. | MR

[9] GEROLDINGER A.-HALTER-KOCH F.-KACZOROWSKI J.: Non-unique factorizations in orders of global fields. J. Reine Angew. Math. 459 (1995), 89-118. | MR | Zbl

[10] GEROLDINGER A.-KACZOROWSKI J.: Analytic and arithmetic theory of semigroups with divisor theory. Sem. Theor. Nombres Bordeaux (2) 4 (1992), 199-238. | MR | Zbl

[11] GEROLDINGER A.-SCHNEIDER R.: On Davenport's constant. J. Combin. Theory Ser. A 61 (1992), 147-152. | MR | Zbl

[12] HALTER-KOCH F.: Chebotarev formations and quantitative aspects of nonunique factorizations. Acta Arith. 62 (1992), 173-206. | MR

[13] HALTER-KOCH F.: Factorization problems in class number two. Colloq. Math. 65 (1993), 255-265. | MR | Zbl

[14] HALTER-KOCH F.: Ideal Systems. An Introduction to Multiplicative Ideal Theory. Pure and Applied Mathematics, Marcel Dekker 211, Marcel Dekker Inc., New York, 1998. | MR | Zbl

[15] KACZOROWSKI J.: Some remarks on factorization in algebraic number fields. Acta Arith. 43 (1983), 53-68. | MR | Zbl

[16] KACZOROWSKI J.-PERELLI A.: Functional independence of the singularities of a class of Dirichlet series. Amer. J. Math. 120 (1998), 289-303. | MR | Zbl

[17] KACZOROWSKI J.-PINTZ J.: Oscillatory properties of arithmetical functions II. Acta Math. Hungar. 49 (1987), 441-453. | MR | Zbl

[18] NARKIEWICZ W.: Finite abelian groups and factorization problems. Colloq. Math. 42 (1979), 319-330. | MR | Zbl

[19] NARKIEWICZ W.-ŚLIWA J.: Finite abelian groups and factorization problems II. Colloq. Math. 46 (1982), 115-122. | MR | Zbl

[20] NARKIEWICZ W.: Elementary and Analytic Theory of Algebraic Numbers. (3rd ed.), Springer-Verlag, Berlin, 2004. | MR | Zbl

[21] NATHANSON M. B.: Additive Number Theory. Grad. Texts in Math. 165, Springer-Verlag, New York, 1996. | MR | Zbl

[22] OLSON J. E.: A combinatorial problem on finite Abelian groups I. J. Number Theory 1 (1969), 8-10. | MR | Zbl

[23] OLSON J. E.: A combinatorial problem on finite Abelian groups II. J. Number Theory 1 (1969), 195-199. | MR | Zbl

[24] RADZIEJEWSKI M.: On the distribution of algebraic numbers with prescribed factorization properties. Acta Arith. 116 (2005), 153-171. | MR | Zbl

[25] RADZIEJEWSKI M.: Oscillations of error terms associated with certain arithmetical functions. Monatsh. Math. (2005) (To appear). | MR | Zbl

[26] RADZIEJEWSKI M.-SCHMID W. A.: On the asymptotic behavior of some counting functions. Colloq. Math. (To appear). | MR | Zbl

[27] SCHMID W. A.: Arithmetic of block monoids. Math. Slovaca 54 (2004), 503-526. | MR | Zbl

[28] SCHMID W. A.: On the asymptotic behavior of some counting functions II. Colloq. Math. (To appear). | MR | Zbl

[29] VAN EMDE BOAS P.-KRUYSWIJK D.: A combinatorial problem on finite abelian groups III. Technical report, Math. Centrum, Amsterdam, Afd. zuivere Wisk. ZW 1969-008. | MR | Zbl