| Title:
|
On invariants related to non-unique factorizations in block monoids and rings of algebraic integers (English) |
| Author:
|
Schmid, Wolfgang A. |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
21-37 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11N64 |
| MSC:
|
11R27 |
| MSC:
|
20D60 |
| MSC:
|
20K01 |
| idZBL:
|
Zbl 1108.11074 |
| idMR:
|
MR2178533 |
| . |
| Date available:
|
2009-09-25T14:24:13Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/129672 |
| . |
| Reference:
|
[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. Zbl 1149.11301, MR 1903437 |
| Reference:
|
[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. Zbl 1061.13001, MR 2140683 |
| Reference:
|
[3] GAO W. D.: On Davenport's constant of finite abelian groups with rank three.Discrete Math. 222 (2000), 111-124. Zbl 0971.20032, MR 1771393 |
| Reference:
|
[4] GAO W. D.: On a combinatorial problem connected with factorizations.Colloq. Math. 72 (1997), 251-268. Zbl 0867.11075, MR 1426700 |
| Reference:
|
[5] GEROLDINGER A.: Ein quantitatives Resultat über Faktorisierungen verschiedener Länge in algebraischen Zahlkörpern.Math. Z. 205 (1990), 159-162. Zbl 0721.11041, MR 1069491 |
| Reference:
|
[6] GEROLDINGER A.-HALTER-KOCH F.: Nonunique factorizations in block semigroups and arithmetical applications.Math. Slovaca 42 (1992), 641-661. MR 1202179 |
| Reference:
|
[7] GEROLDINGER A.-HALTER-KOCH F.: Congruence monoids.Acta Arith. 112 (2004), 263-296. Zbl 1057.13003, MR 2046184 |
| Reference:
|
[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 2140689 |
| Reference:
|
[9] GEROLDINGER A.-HALTER-KOCH F.-KACZOROWSKI J.: Non-unique factorizations in orders of global fields.J. Reine Angew. Math. 459 (1995), 89-118. Zbl 0812.11061, MR 1319518 |
| Reference:
|
[10] GEROLDINGER A.-KACZOROWSKI J.: Analytic and arithmetic theory of semigroups with divisor theory.Sem. Theor. Nombres Bordeaux (2) 4 (1992), 199-238. Zbl 0780.11046, MR 1208863 |
| Reference:
|
[11] GEROLDINGER A.-SCHNEIDER R.: On Davenport's constant.J. Combin. Theory Ser. A 61 (1992), 147-152. Zbl 0759.20008, MR 1178393 |
| Reference:
|
[12] HALTER-KOCH F.: Chebotarev formations and quantitative aspects of nonunique factorizations.Acta Arith. 62 (1992), 173-206. MR 1183988 |
| Reference:
|
[13] HALTER-KOCH F.: Factorization problems in class number two.Colloq. Math. 65 (1993), 255-265. Zbl 0816.11053, MR 1240171 |
| Reference:
|
[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. Zbl 0953.13001, MR 1828371 |
| Reference:
|
[15] KACZOROWSKI J.: Some remarks on factorization in algebraic number fields.Acta Arith. 43 (1983), 53-68. Zbl 0526.12006, MR 0730848 |
| Reference:
|
[16] KACZOROWSKI J.-PERELLI A.: Functional independence of the singularities of a class of Dirichlet series.Amer. J. Math. 120 (1998), 289-303. Zbl 0905.11036, MR 1613634 |
| Reference:
|
[17] KACZOROWSKI J.-PINTZ J.: Oscillatory properties of arithmetical functions II.Acta Math. Hungar. 49 (1987), 441-453. Zbl 0631.10026, MR 0891057 |
| Reference:
|
[18] NARKIEWICZ W.: Finite abelian groups and factorization problems.Colloq. Math. 42 (1979), 319-330. Zbl 0514.12004, MR 0567570 |
| Reference:
|
[19] NARKIEWICZ W.-ŚLIWA J.: Finite abelian groups and factorization problems II.Colloq. Math. 46 (1982), 115-122. Zbl 1164.20358, MR 0672371 |
| Reference:
|
[20] NARKIEWICZ W.: Elementary and Analytic Theory of Algebraic Numbers.(3rd ed.), Springer-Verlag, Berlin, 2004. Zbl 1159.11039, MR 2078267 |
| Reference:
|
[21] NATHANSON M. B.: Additive Number Theory.Grad. Texts in Math. 165, Springer-Verlag, New York, 1996. Zbl 0859.11003, MR 1395371 |
| Reference:
|
[22] OLSON J. E.: A combinatorial problem on finite Abelian groups I.J. Number Theory 1 (1969), 8-10. Zbl 0169.02003, MR 0237641 |
| Reference:
|
[23] OLSON J. E.: A combinatorial problem on finite Abelian groups II.J. Number Theory 1 (1969), 195-199. Zbl 0167.28004, MR 0240200 |
| Reference:
|
[24] RADZIEJEWSKI M.: On the distribution of algebraic numbers with prescribed factorization properties.Acta Arith. 116 (2005), 153-171. Zbl 1136.11064, MR 2110393 |
| Reference:
|
[25] RADZIEJEWSKI M.: Oscillations of error terms associated with certain arithmetical functions.Monatsh. Math. (2005) (To appear). Zbl 1099.11056, MR 2123959 |
| Reference:
|
[26] RADZIEJEWSKI M.-SCHMID W. A.: On the asymptotic behavior of some counting functions.Colloq. Math. (To appear). Zbl 1143.11346, MR 2152660 |
| Reference:
|
[27] SCHMID W. A.: Arithmetic of block monoids.Math. Slovaca 54 (2004), 503-526. Zbl 1108.11084, MR 2114621 |
| Reference:
|
[28] SCHMID W. A.: On the asymptotic behavior of some counting functions II.Colloq. Math. (To appear). Zbl 1143.11351, MR 2152661 |
| Reference:
|
[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. Zbl 0245.20046, MR 0255672 |
| . |
