Analytic and arithmetic theory of semigroups with divisor theory
Journal de Théorie des Nombres de Bordeaux, Tome 4 (1992) no. 2, pp. 199-238.
@article{JTNB_1992__4_2_199_0,
     author = {Geroldinger, Alfred and Kaczorowski, Jerzy},
     title = {Analytic and arithmetic theory of semigroups with divisor theory},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {199--238},
     publisher = {Universit\'e Bordeaux I},
     volume = {4},
     number = {2},
     year = {1992},
     doi = {10.5802/jtnb.72},
     zbl = {0780.11046},
     mrnumber = {1208863},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.72/}
}
Alfred Geroldinger; Jerzy Kaczorowski. Analytic and arithmetic theory of semigroups with divisor theory. Journal de Théorie des Nombres de Bordeaux, Tome 4 (1992) no. 2, pp. 199-238. doi : 10.5802/jtnb.72. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.72/

[Ch] L.G. Chouinardii, Krull semigroups and divisor class groups, Canad. J. Math. 33 (1981), 1459-1468. | MR 645239 | Zbl 0453.13005

[C-P] A.H. Clifford and G.B. Preston, The algebraic theory of semigroups, Vol. II, Providence, Rhode Island 1967. | MR 218472 | Zbl 0178.01203

[F-S] W. Forman and H.N. Shapiro, Abstract prime number theorems, Comm. Pure Appl. Math. 7 (1954), 587-619. | MR 63396 | Zbl 0057.28404

[Ge1] A. Geroldinger, Über nicht-eindeutige Zerlegungen in irreduzible Elemente, Math. Z. 197 (1988), 505-529. | MR 932683 | Zbl 0618.12002

[Ge2] A. Geroldinger, Factorizations of algebraic integers, Number Theory, Ulm 1987, Springer Lecture Notes 1380, 63-74. | MR 1009793 | Zbl 0684.12007

[Ge3] A. Geroldinger, Factorization of natural numbers in algebraic number fields, Acta Arith. 57 (1991), 365-373. | MR 1109993 | Zbl 0729.11054

[Ge-HK] A. Geroldinger and F. Halter-Koch, Realization theorems of semigroups with divisor theory, Semigroup Forum 44 (1992), 229-237. | MR 1141841 | Zbl 0751.20045

[Gi] R. Gilmer, Commutative Semigroup Rings, The University of Chicago Press 1984. | MR 741678 | Zbl 0566.20050

[HK1] F. Halter-Koch, Halbgruppen mit Divisorentheorie, Expo. Math. 8 (1990), 27-66. | MR 1042201 | Zbl 0698.20054

[HK2] F. Halter-Koch, Ein Approximationssatz für Halbgruppen mit Divisorentheorie, Resultate der Math. 19 (1991), 74-82. | MR 1091957 | Zbl 0742.20060

[HK3] F. Halter-Koch, A generalization of Davenport's constant and its arithmetical applications, Coll. Math. 63 (1992), 203-210. | MR 1180633 | Zbl 0760.11031

[HK-M] F. Halter-Koch and W. Müller, Quantitative aspects of non-unique factorization: a general theory with applications to algebraic function fields, J. Reine Angew. Math 421 (1991), 159-188. | MR 1129580 | Zbl 0736.11064

[Ka] J. Kaczorowski, Some remarks on factorization in algebraic number fields, Acta Arith. 43 (1983), 53-68. | MR 730848 | Zbl 0526.12006

[Kr] U. Krause, On monoids of finite real character, Proc. AMS 105 (1989), 546-554. | MR 953009 | Zbl 0692.20058

[La] S. Lang, Algebraic Number Theory, Springer 1986. | MR 1282723 | Zbl 0601.12001

[Le] G. Lettl, Durch Normen definierte Idealklassengruppen, Studia Sci. Math. Hungarica 23 (1988), 327-334. | MR 982680 | Zbl 0677.12002

[M] M. Mazur, A note on the growth of Davenport's constant, Manuscripta Math. 74 (1992), 229-235. | MR 1149760 | Zbl 0759.20009

[N] W. Narkiewicz, Finite abelian groups and factorization problems, Coll. Math. 42 (1979), 319-330. | MR 567570 | Zbl 0514.12004

[P] K. Prachar, Primzahlverteilung, Springer 1978. | MR 516660 | Zbl 0394.10001

[Sk] L. Skula, On c-semigroups, Acta Arith. 31 (1976), 247-257. | MR 444817 | Zbl 0303.13014

[Sl] J. Sliwa, Remarks on factorizations in algebraic number fields, Coll. Math. 46 (1982), 123-130. | MR 672372 | Zbl 0514.12005

[S-Z] S. Saks and A. Zygmund, Analytic functions, Polish Scientific Publishers 1965. | MR 180658 | Zbl 0136.37301

[T1] E.C. Titchmarsh, The theory of functions, Oxford University Press 1964. | MR 197687

[T2] E.C. Titchmarsh, The theory of the Riemann zeta function, Oxford at the Clarendon Press 1986. | MR 882550 | Zbl 0601.10026