BOOKS:

A. Geroldinger and F. Halter-Koch. Non-Unique Factorizations: Algebraic, Combinatorial and Analytic Theory, volume 278 of Pure and Applied Mathematics. Chapman & Hall/CRC, 2006.

PAPERS:

[1]     A. Geroldinger. Über nicht-eindeutige Zerlegungen in irreduzible Elemente. Math. Z., 197:505 - 529, 1988.

[2]     A. Geroldinger. Factorizations of algebraic numbers. In Number Theory, Ulm, volume 1380 of Lecture Notes in Math., pages 63 - 74. Springer, 1989.

[3]     A. Geroldinger and G. Lettl. Factorization problems in semigroups. Semigroup Forum, 40:23 - 38, 1990.

[4]     A. Geroldinger. Arithmetical characterizations of divisor class groups. Arch. Math., 54:455 - 464, 1990.

[5]     A. Geroldinger. Ein quantitatives Resultat über Faktorisierungen verschiedener Länge in algebraischen Zahlkörpern. Math. Z., 205:159 - 162, 1990.

[6]     A. Geroldinger. Systeme von Längenmengen. Abh. Math. Semin. Univ. Hamb., 60:115 - 130, 1990.

[7]     A. Geroldinger. On non-unique factorizations into irreducible elements. II. In Number Theory, Vol. II Budapest 1987, 

        volume 51 of Colloquia Mathematica      Societatis Janos Bolyai, pages 723 - 757. North Holland, 1990.

[8]     A. Geroldinger. Factorization of natural numbers in algebraic number fields. Acta Arith., 57:365 - 373, 1991.

[9]     A. Geroldinger. On the arithmetic of certain not integrally closed noetherian integral domains. Commun. Algebra, 19:685 - 698, 1991.

[10]   A. Geroldinger and F. Halter-Koch. Realization theorems for semigroups with divisor theory. Semigroup Forum, 44:229 - 237, 1992.

[11]   A. Geroldinger and F. Halter-Koch. On the asymptotic behaviour of lengths of factorizations. J. Pure Appl. Algebra, 77:239 - 252, 1992.

[12]   A. Geroldinger and F. Halter-Koch. Non-unique factorizations in block semigroups and arithmetical applications. Math. Slovaca, 42:641 - 661, 1992.

[13]   A. Geroldinger. Arithmetical characterizations of divisor class groups II. Acta Math. Univ. Comen., New Ser., 61:193 - 208, 1992.

[14]   A. Geroldinger and R. Schneider. On Davenport's constant. J. Comb. Theory, Ser. A, 61:147 - 152, 1992.

[15]   A. Geroldinger and J. Kaczorowski. Analytic and arithmetic theory of semigroups with divisor theory. J. Théor. Nombres Bordx., 4:199 - 238, 1992.

[16]   A. Geroldinger. On a conjecture of Kleitman and Lemke. J. Number Theory, 44:60 - 65, 1993.

[17]    A. Geroldinger. The complete integral closure of monoids and domains. PU.M.A., Pure Math. Appl., 4:147 - 165, 1993.

[18]    A. Geroldinger and F. Halter-Koch. Arithmetical theory of monoid homomorphisms. Semigroup Forum, 48:333 - 362, 1994.

[19]    A. Geroldinger. T-block monoids and their arithmetical applications to certain integral domains. Commun. Algebra, 22:1603 - 1615, 1994.

[20]    A. Geroldinger. The cross number of finite abelian groups. J. Number Theory, 48:219 - 223, 1994.

[21]    A. Geroldinger and R. Schneider. The cross number of finite abelian groups II. Eur. J. Comb., 15:399 - 405, 1994.

[22]    A. Geroldinger, F. Halter-Koch, and J. Kaczorowski. Non-unique factorizations in orders of global fields. J. Reine Angew. Math., 459:89 - 118, 1995.

[23]    A. Geroldinger, F. Halter-Koch, and G. Lettl. The complete integral closure of monoids and domains II. Rend. Mat. Appl., VII. Ser., 15:281 - 292, 1995.

[24]    A. Geroldinger and J. Mockor. Quasi divisor theories and generalizations of Krull domains. J. Pure Appl. Algebra, 102:289 - 311, 1995.

[25]    A. Geroldinger. On the structure and arithmetic of finitely primary monoids. Czech. Math. J., 46:677 - 695, 1996.

[26]    A. Geroldinger and F. Halter-Koch. On quasi divisor theories and systems of valuations. Monatsh. Math., 121:55 - 67, 1996.

[27]    S.T. Chapman and A. Geroldinger. On cross numbers of minimal zero sequences. Australas. J. Comb., 14:85 - 92, 1996.

[28     A. Geroldinger and R. Schneider. The cross number of finite abelian groups III. Discrete Math., 150:123 - 130, 1996.

[29]    A. Geroldinger. Chains of factorizations in weakly Krull domains. Colloq. Math., 72:53 - 81, 1997.

[30]    A. Geroldinger. Chains of factorizations in orders of global fields. Colloq. Math., 72:83 - 102, 1997.

[31]    A. Geroldinger. Chains of factorizations and sets of lengths. J. Algebra, 188:331 - 363, 1997.

[32]    A. Geroldinger. The catenary degree and tameness of factorizations in weakly Krull domains. In Factorization in Integral Domains, 

         volume 189 of Lect. Notes Pure Appl. Math., pages 113 - 153. Marcel Dekker, 1997.

[33]    S.T. Chapman and A. Geroldinger. Krull domains and monoids, their sets of lengths and associated combinatorial problems.

          In Factorization in Integral Domains, volume 189 of Lect. Notes Pure Appl. Math., pages 73 - 112. Marcel Dekker, 1997.

[34]    A. Geroldinger and R. Schneider. On minimal zero sequences with large cross number. Ars Comb., 46:297 - 303, 1997.

[35]    A. Geroldinger. A structure theorem for sets of lengths. Colloq. Math., 78:225 - 259, 1998.

[36]    W. Gao and A. Geroldinger. On the structure of zerofree sequences. Combinatorica, 18:519 - 527, 1998.

[37]    W. Gao and A. Geroldinger. Half-factorial domains and half-factorial subsets in abelian groups. Houston J. Math., 24:593 - 611, 1998.

[38]    W. Gao and A. Geroldinger. On long minimal zero sequences in finite abelian groups. Period. Math. Hung., 38:179 - 211, 1999.

[39]    W. Gao and A. Geroldinger. Systems of sets of lengths II. Abh. Math. Semin. Univ. Hamb., 70:31 - 49, 2000.

[40]   G.A. Freiman and A. Geroldinger. An addition theorem and its arithmetical application. J. Number Theory, 85:59 - 73, 2000.

[41]   W. Gao and A. Geroldinger. On the order of elements in long minimal zero-sum sequences. Period. Math. Hung., 44:63 - 73, 2002.

[42]    A. Geroldinger and Y. ould Hamidoune. Zero-sumfree sequences in cyclic groups and some arithmetical application. 

         J. Théor. Nombres Bordx., 14:221 - 239, 2002.

[43]   A. Geroldinger and F. Halter-Koch. Tamely generated ideals in finitary monoids. JP J. Algebra Number Theory Appl., 2:205 - 239, 2002.

[44]   A. Geroldinger, F. Halter-Koch, W. Hassler, and F. Kainrath. Finitary monoids. Semigroup Forum, 67:1 - 21, 2003.

[45]   A. Geroldinger and R. Göbel. Half-factorial subsets in infinite abelian groups. Houston J. Math., 29:841 - 858, 2003.

[46]   W. Gao and A. Geroldinger. Zero-sum problems and coverings by proper cosets. Eur. J. Comb., 24:531 - 549, 2003.

[47]    W. Gao and A. Geroldinger. On zero-sum sequences in Z /n Z x Z /n Z. Integers, 3:Paper A08, 45p, 2003.

[48]    A. Geroldinger and F. Halter-Koch. Congruence monoids. Acta Arith., 112:263 - 296, 2004.

[49]    A. Geroldinger and F. Halter-Koch. Transfer principles in the theory of non-unique factorizations. In Arithmetical Properties of Commutative Rings and Monoids,          volume 241 of Lecture Notes in Pure Appl. Math., pages 114 - 142. Chapman & Hall/CRC, 2005.

[50]    A. Foroutan and A. Geroldinger. Monotone chains of factorizations in C-monoids. In Arithmetical Properties of Commutative Rings and Monoids, 

         volume 241 of Lecture Notes in Pure Appl. Math., pages 99 - 113. Chapman & Hall/CRC, 2005.

[51]   W. Gao and A. Geroldinger. On a property of minimal zero-sum sequences and restricted sumsets. Bull. Lond. Math. Soc., 37:321 - 334, 2005.

[52]    R. Chi, S. Ding, W. Gao, A. Geroldinger, and W.A. Schmid. On zero-sum subsequences of restricted size IV. Acta Math. Hung., 107:337 - 344, 2005.

[53]    W. Gao and A. Geroldinger. On the number of subsequences with given sum of sequences over finite abelian p-groups. 

         Rocky Mt. J. Math., 37: 1541 -- 1550, 2007.

[54]     A. Geroldinger and F. Halter-Koch. Non-Unique Factorizations : a survey. In J.W. Brewer, S. Glaz, W. Heinzer, and B. Olberding, editors, 

          Multiplicative Ideal Theory in Commutative Algebra, 217 - 226, Springer 2006.

[55]    W. Gao and A. Geroldinger. Zero-sum problems in abelian groups : a survey. Expo. Math., 24:337 -- 369, 2006.

[56]    Y. Edel, C. Elsholtz, A. Geroldinger, S. Kubertin and L. Rackham. Zero-sum problems in finite abelian groups and affine caps. 

         Quarterly J. Math., Oxford II. Ser., 58:159 -- 186, 2007.

[57]    W. Gao, A. Geroldinger, and F. Halter-Koch. Group algebras of finite abelian groups and their applications to combinatorial problems, 

         Rocky Mt. J. Math.,  39:805 -- 823, 2009.

[58]    W. Gao, A. Geroldinger and W.A. Schmid. Inverse zero-sum problems. Acta Arith., 128:245 -- 279, 2007.

[59]    A. Geroldinger, W. Hassler and G. Lettl. On the arithmetic of strongly primary monoids. Semigroup Forum, 75: 567 -- 587, 2007.

[60]    A. Geroldinger and W. Hassler. Local tameness of v-noetherian monoids. J. Pure Appl. Algebra, 212:1509 -- 1524, 2008.

[61]    A. Geroldinger and W. Hassler. Arithmetic of Mori domains and monoids. J. Algebra, 319:3419 -- 3463, 2008.

[62]    M. Freeze and A. Geroldinger. Unions of sets of lengths. Funct. Approximatio, Comment. Math., 39:149 -- 162, 2008.

[63]    W. Gao and A. Geroldinger. On products of k-atoms. Monatsh. Math., 156: 141 -- 157, 2009.

[64]    A. Geroldinger. Additive group theory and non-unique factorizations. In A. Geroldinger and I. Ruzsa, Combinatorial Number Theory and Additive Group Theory,                    1 - 86, Advanced Courses in Mathematics, CRM Barcelona, Birkhäuser 2009. 

[65]    A. Geroldinger and D.J. Grynkiewicz. On the arithmetic of Krull monoids with finite Davenport constant. J. Algebra, 321:1256 -- 1284, 2009.

[66]    A. Geroldinger and D.J.  Grynkiewicz. On the structure of minimal zero-sum sequences with maximal cross number. 

         Journal of Combinatorics and Number  Theory, 1(2): 9 -- 26, 2009.

[67]    M. Freeze, W. Gao and A. Geroldinger. The critical number of finite abelian groups.  J. Number Theory, 129:2766 -- 2777, 2009.

[68]   W.Gao, A. Geroldinger and D. Grynkiewicz.  Inverse zero-sum problems III. Acta Arith., 141: 103 -- 152, 2010.

[69]    A. Geroldinger and F. Kainrath. On the arithmetic of tame monoids with applications to Krull monoids and Mori domains. 

         J. Pure Appl. Algebra, 214: 2199 -- 2218, 2010.

[70]   A. Geroldinger, D.J. Grynkiewicz, G.J. Schaeffer and W.A. Schmid. On the arithmetic of  Krull monoids with infinite cyclic class group.

        J. Pure Appl. Algebra, 214: 2219 -- 2250, 2010.

[71]   A. Geroldinger, D.J. Grynkiewicz and W.A. Schmid. The catenary degree of  Krull monoids I. 

        J. Theor. Nombres Bordx., 23:  137 -- 169, 2011.

[72]   A. Geroldinger, D.J. Grynkiewicz and W.A. Schmid. Zero-sum problems with congruence conditions. 

        Acta Math. Hung., 131:  323 -- 345, 2011.

[73]    A. Geroldinger,  M. Liebmann and A. Philipp. On the Davenport constant and on the structure of extremal zero-sum free sequences, Period. Math. Hung., 

[74]    W.  Gao, A. Geroldinger and Qinghong Wang. A quantitative aspect of non-unique factorizations: the Narkiewicz constants.     

          Int. J. Number Theory, 7: 1463 -- 1502, 2011.

[75]    V.  Blanco, P.A. Garcia-Sanchez and A. Geroldinger.

          Semigroup theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids.

Illinois Journal of Mathematics, to appear

[76]    A. Geroldinger. Non-commutative Krull monoids: a divisor theoretic approach and their arithmetic. Osaka J. Mathematics, to appear.

[77]    P. Baginski, A. Geroldinger, D.J. Grynkiewicz and A. Philipp.  Products of two atoms in Krull monoids and arithmetical  characterizations of class groups. .

[78]    A. Geroldinger and P. Yuan. The set of distances in Krull monoids. 

[79]    A. Geroldinger and P. Yuan. The monotone catenary degree of Krull monoids. .