Reminder

In all DK related publications, it is required to acknowledge support of the FWF. The following naming convention must be used in all cases:

    Austrian Science Fund (FWF): W1230

For example, you may include a sentence such as "The author acknowledges the support of the Austrian Science Fund (FWF): W1230." Please do not forget!

Project 3:
Additive theory, zero-sum theory and non-unique factorizations

2010
[31]Daniel Smertnig, On the Davenport constant and group algebras, Colloquium Mathematicum, 121(2), 179 – 193, (2010). [bibtex] [doi]
2012
[30]Alfred Geroldinger and Pingzhi Yuan, The set of distances in Krull monoids, Bulletin of the London Mathematical Society, 44(6), 1203 – 1208, (2012). [bibtex] [doi]
2013
[29]Gyu Whan Chang and Daniel Smertnig, Factorization in the self-idealization of a PID, Boll. Unione Mat. Ital. (9), 6(2), 363 – 377, (2013). [bibtex]
[28]Alfred Geroldinger and Pingzhi Yuan, The monotone catenary degree of Krull monoids, Results in Mathematics, 63(3-4), 999 – 1031, (2013). [bibtex] [pdf] [doi]
[27]Daniel Smertnig, Sets of lengths in maximal orders in central simple algebras, Journal of Algebra, 390, 1 – 43, (2013). [bibtex] [doi]
[26]Daniel Smertnig, A note on cancellation in totally definite quaternion algebras, Journal fürr die Reine und Angewandte Mathematik, 707, 209 – 216, (2013). [bibtex] [pdf] [doi]
2014
[25]Alberto Facchini, Nguyen Khanh Tung and Daniel Smertnig, Cyclically presented modules, projective covers and factorizations, In Ring Theory and its Applications (Dinh Van Huynh, others, eds.), Amer. Math. Soc., 609, 89 – 106, (2014). [bibtex] [doi]
[24]Daniel Smertnig, Factorization theory in maximal orders, PhD thesis, KFU Graz, (2014). [bibtex] [url]
2015
[23]Nicholas R. Baeth, Alfred Geroldinger, David Grynkiewicz and Daniel Smertnig, A semigroup-theoretical view of direct-sum decompositions and associated combinatorial problems, Journal of Algebra and its Applications, 14(2), article No.\ 1550016, 60 pp., (2015). [bibtex] [doi]
[22]Nicholas R. Baeth and Daniel Smertnig, Factorization Theory: from commutative to noncommutative settings, Journal of Algebra, 441, 475 – 551, (2015). [bibtex] [doi]
2016
[21]Scott T. Chapman, Marco Fontana, Alfred Geroldinger and Bruce Olberding, Multiplicative Ideal Theory and Factorization Theory, Springer Proceedings in Mathematics &\ Statistics, 170, (2016). [bibtex] [doi]
2019
[20]Jun Seok Oh, On the algebraic and arithmetic structure of the monoid of product-one sequences II, Periodica Mathematica Hungarica, 78(2), 203 – 230, (2019). [bibtex] [doi]
[19]Jun Seok Oh, Product-one Sequences over Finite Groups: Algebraic, Arithmetic, and Combinatorial Aspects, PhD thesis, KFU Graz, (2019). [bibtex] [url]
[18]Jun Seok Oh and Qinghai Zhong, On minimal product-one sequences of maximal length over Dihedral and Dicyclic groups, Communications of the Korean Mathematical Society, 35(1), 83 – 116, (2019). [bibtex] [doi]
2020
[17]Advances in Rings, Modules, and Factorizations, (Alberto Facchini, Marco Fontana, Alfred Geroldinger, Bruce Olberding, eds.), 321, (2020). [bibtex] [url]
[16]Alfred Geroldinger and Qinghai Zhong, Factorization Theory in Commutative Monoids, Semigroup Forum, 100, 22 – 51, (2020). [bibtex] [doi]
[15]Jun Seok Oh, On the algebraic and arithmetic structure of the monoid of product-one sequences, Journal of Commutative Algebra, 12(3), 409 – 433, (2020). [bibtex] [doi]
[14]Jun Seok Oh and Qinghai Zhong, On Erd\H os-Ginzburg-Ziv inverse theorems for dihedral and dicyclic groups, Israel Journal of Mathematics, 238, 715 – 743, (2020). [bibtex] [doi]
2021
[13]Casper Barendrecht, Elasticities of orders in central simple algebras, (2021). (Acta Arith.) [bibtex]
[12]Aqsa Bashir, Alfred Geroldinger and Qinghai Zhong, On a zero-sum problem arising from factorization theory, In Combinatorial and Additive Number Theory IV (M. Nathanson, ed.), Springer, 11-24, (2021). [bibtex] [doi]
[11]Aqsa Bashir, Alfred Geroldinger and Andreas Reinhart, On the arithmetic of stable domains, Communications in Algebra, 49(11), 4763 – 4787, (2021). [bibtex] [doi]
2022
[10]Aqsa Bashir and Andreas Reinhart, On transfer Krull monoids, (2022). (Semigroup Forum) [bibtex] [url]
[9]Gyu Whan Chang, Victor Fadinger and Daniel Windisch, Semigroup rings as weakly Krull domains, (2022). (Pacific J. Math.) [bibtex]
[8]Victor Fadinger, Sophie Frisch and Daniel Windisch, Integer-valued polynomials on discrete valuation rings of global fields with prescribed lengths of factorizations, (2022). (submitted) [bibtex]
[7]Victor Fadinger, On Monoid Algebras: Algebraic and Arithmetic Properties, PhD thesis, KFU Graz, (2022). [bibtex] [url]
[6]Victor Fadinger and Daniel Windisch, A characterization of weakly Krull monoid algebras, Journal of Algebra, 590, 277 – 292, (2022). [bibtex] [doi]
[5]Victor Fadinger and Daniel Windisch, On the distribution of prime divisors in Krull monoid algebras, Journal of Pure and Applied Algebra, 22(4), Paper No. 106887, 8 pp, (2022). [bibtex] [doi]
[4]Victor Fadinger and Daniel Windisch, On the distribution of prime divisors in class groups of affine monoid algebras, Communications in Algebra, 50(7), 2973 – 2982, (2022). [bibtex] [doi]
[3]Victor Fadinger and Qinghai Zhong, On product-one sequences over subsets of groups, Periodica Mathematica Hungarica, (2022). (to appear) [bibtex]
[2]Alfred Geroldinger, David Grynkiewicz, Jun Seok Oh and Qinghai Zhong, On product-one sequences over dihedral groups, Journal of Algebra and its Applications, 2250064,1–58, (2022). [bibtex] [doi]
[1]Salvatore Tringali, An abstract factorization theorem and some applications, Journal of Algebra, 602, 352 – 380, (2022). [bibtex] [doi]