@article{bwmeta1.element.bwnjournal-article-cmv78z2p225bwm, author = {Alfred Geroldinger}, title = {A structure theorem for sets of lengths}, journal = {Colloquium Mathematicae}, volume = {78}, year = {1998}, pages = {225-259}, zbl = {0926.11082}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv78z2p225bwm} }
Geroldinger, Alfred. A structure theorem for sets of lengths. Colloquium Mathematicae, Tome 78 (1998) pp. 225-259. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv78z2p225bwm/
[000] [An] D. D. Anderson (ed.), Factorization in Integral Domains, Lecture Notes in Pure and Appl. Math. 189, Marcel Dekker, 1997.
[001] [A-M-Z] D. D. Anderson, J. L. Mott and M. Zafrullah, Finite character representations for integral domains, Boll. Un. Mat. Ital. B (7) 6 (1992), 613-630. | Zbl 0773.13004
[002] [Bo] N. Bourbaki, Commutative Algebra, Springer, 1989.
[003] [Cha-Ge] S. Chapman and A. Geroldinger, Krull domains and monoids, their sets of lengths and associated combinatorial problems, in: [An], 73-112. | Zbl 0897.13001
[004] [Ge1] A. Geroldinger, Über nicht-eindeutige Zerlegungen in irreduzible Elemente, Math. Z. 197 (1988), 505-529.
[005] [Ge2] A. Geroldinger, Chains of factorizations in weakly Krull domains, Colloq. Math. 72 (1997), 53-81. | Zbl 0874.13001
[006] [Ge3] A. Geroldinger, Chains of factorizations and sets of lengths, J. Algebra 188 (1997), 331-362. | Zbl 0882.20039
[007] [Ge4] A. Geroldinger, The catenary degree and tameness of factorizations in weakly Krull domains, in: [An], 113-153. | Zbl 0897.13002
[008] [Ge5] A. Geroldinger, On the structure and arithmetic of finitely primary monoids, Czechoslovak Math. J. 46 (1996), 677-695. | Zbl 0879.20032
[009] [Ge6] A. Geroldinger, T-block monoids and their arithmetical applications to certain integral domains, Comm. Algebra 22 (1994), 1603-1615. | Zbl 0809.13013
[010] [G-L] A. Geroldinger and G. Lettl, Factorization problems in semigroups, Semigroup Forum 40 (1990), 23-38. | Zbl 0693.20063
[011] [Gi] R. Gilmer, Commutative Semigroup Rings, The University of Chicago Press, 1984.
[012] [HK1] F. Halter-Koch, Über Längen nicht-eindeutiger Faktorisierungen und Systeme linearer diophantischer Ungleichungen, Abh. Math. Sem. Univ. Hamburg 63 (1993), 265 -276.
[013] [HK2] F. Halter-Koch, Finitely generated monoids, finitely primary monoids and factorization properties of integral domains, in: [An], 31-72. | Zbl 0882.13027
[014] [HK3] F. Halter-Koch, The integral closure of a finitely generated monoid and the Frobenius problem in higher dimensions, in: Semigroups, C. Bonzini, A. Cherubini and C. Tibiletti (eds.), World Scientific, 1993, 86-93. | Zbl 0818.20079
[015] [HK4] F. Halter-Koch, Finiteness theorems for factorizations, Semigroup Forum 44 (1992), 112-117. | Zbl 0751.20046
[016] [HK5] F. Halter-Koch, Divisor theories with primary elements and weakly Krull domains, Boll. Un. Mat. Ital. B (7) 9 (1995), 417-441. | Zbl 0849.20041
[017] [HK6] F. Halter-Koch, Elasticity of factorizations in atomic monoids and integral domains, J. Théor. Nombres Bordeaux 7 (1995), 367-385. | Zbl 0844.11068
[018] [Ka] F. Kainrath, Factorization in Krull monoids with infinite class group. | Zbl 0936.20050
[019] [Na1] W. Narkiewicz, Finite abelian groups and factorization problems, Colloq. Math. 42 (1979), 319-330. | Zbl 0514.12004
[020] [Sc] H. Scheid, Zahlentheorie, 2. Auflage, B.I. Wissenschaftsverlag, 1994.
[021] [Sl] J. Śliwa, Remarks on factorizations in algebraic number fields, Colloq. Math. 46 (1982), 123-130. | Zbl 0514.12005
[022] [Wa] L. C. Washington, Introduction to Cyclotomic Fields, 2nd ed., Springer, 1997. | Zbl 0966.11047