1 |
Y. Fan, A. Geroldinger, F. Kainrath, and S. Tringali, Arithmetic of commutative semi-groups with a focus on semigroups of ideals and modules, J. Algebra Appl. 16 (2017), no. 12, 1750234, 42 pp. https://doi.org/10.1142/S0219498817502346
DOI
|
2 |
Y. Fan and S. Tringali, Power monoids: a bridge between factorization theory and arithmetic combinatorics, J. Algebra 512 (2018), 252-294. https://doi.org/10.1016/j. jalgebra.2018.07.010
DOI
|
3 |
W. Gao and A. Geroldinger, Zero-sum problems in finite abelian groups: a survey, Expo. Math. 24 (2006), no. 4, 337-369. https://doi.org/10.1016/j.exmath.2006.07.002
DOI
|
4 |
W. Gao, A. Geroldinger, and D. J. Grynkiewicz, Inverse zero-sum problems III, Acta Arith. 141 (2010), no. 2, 103-152. https://doi.org/10.4064/aa141-2-1
DOI
|
5 |
W. Gao, A. Geroldinger, and W. A. Schmid, Inverse zero-sum problems, Acta Arith. 128 (2007), no. 3, 245-279. https://doi.org/10.4064/aa128-3-5
DOI
|
6 |
A. Geroldinger, Additive group theory and non-unique factorizations, in Combinatorial number theory and additive group theory, 1-86, Adv. Courses Math. CRM Barcelona, Birkhauser Verlag, Basel, 2009. https://doi.org/10.1007/978-3-7643-8962-8
|
7 |
A. Geroldinger and D. J. Grynkiewicz, The large Davenport constant I: Groups with a cyclic, index 2 subgroup, J. Pure Appl. Algebra 217 (2013), no. 5, 863-885. https://doi.org/10.1016/j.jpaa.2012.09.004
DOI
|
8 |
A. Geroldinger and F. Halter-Koch, Non-Unique Factorizations, Pure and Applied Mathematics (Boca Raton), 278, Chapman & Hall/CRC, Boca Raton, FL, 2006. https://doi.org/10.1201/9781420003208
|
9 |
A. Geroldinger, F. Kainrath, and A. Reinhart, Arithmetic of seminormal weakly Krull monoids and domains, J. Algebra 444 (2015), 201-245. https://doi.org/10.1016/j. jalgebra.2015.07.026
DOI
|
10 |
A. Geroldinger and Q. Zhong, A characterization of seminormal C-monoids, Boll. Unione Mat. Ital., to appear; https://doi.org/10.1007/s40574-019-00194-9
|
11 |
D. J. Grynkiewicz, The large Davenport constant II: general upper bounds, J. Pure Appl. Algebra 217 (2013), no. 12, 2221-2246. https://doi.org/10.1016/j.jpaa.2013.03.002
DOI
|
12 |
B. Girard, An asymptotically tight bound for the Davenport constant, J. Ec. polytech. Math. 5 (2018), 605-611. https://doi.org/10.5802/jep.79
DOI
|
13 |
B. Girard and W. A. Schmid, Inverse zero-sum problems for certain groups of rank three, submitted; https://arxiv.org/abs/1809.03178.
|
14 |
B. Girard and W. A. Schmid, Direct zero-sum problems for certain groups of rank three, J. Number Theory 197 (2019), 297-316. https://doi.org/10.1016/j.jnt.2018.08.016
DOI
|
15 |
J. S. Oh, On the algebraic and arithmetic structure of the monoid of product-one sequences II, Period. Math. Hungar. 78 (2019), 203-230.
DOI
|
16 |
D. J. Grynkiewicz, Structural Additive Theory, Developments in Mathematics, 30, Springer, Cham, 2013. https://doi.org/10.1007/978-3-319-00416-7
|
17 |
D. Han and H. Zhang, Erdos-Ginzburg-Ziv theorem and Noether number for , J. Number Theory 198 (2019), 159-175. https://doi.org/10.1016/j.jnt.2018.10.007
DOI
|
18 |
J. S. Oh, On the algebraic and arithmetic structure of the monoid of product-one sequences, J. Commut. Algebra, to appear; https://projecteuclid.org/euclid.jca/1523433705
|
19 |
W. A. Schmid, Inverse zero-sum problems II, Acta Arith. 143 (2010), no. 4, 333-343. https://doi.org/10.4064/aa143-4-2
DOI
|
20 |
W. A. Schmid, The inverse problem associated to the Davenport constant for , and applications to the arithmetical characterization of class groups, Electron. J. Combin. 18 (2011), no. 1, Paper 33, 42 pp.
|
21 |
K. Cziszter and M. Domokos, On the generalized Davenport constant and the Noether number, Cent. Eur. J. Math. 11 (2013), no. 9, 1605-1615. https://doi.org/10.2478/s11533-013-0259-z
|
22 |
W. A. Schmid, Some recent results and open problems on sets of lengths of Krull monoids with finite class group, in Multiplicative ideal theory and factorization theory, 323-352, Springer Proc. Math. Stat., 170, Springer, 2016. https://doi.org/10.1007/978-3-319-38855-7_14
|
23 |
S. Tringali, Structural properties of subadditive families with applications to factorization theory, Israel J. Math., to appear; https://arxiv.org/abs/1706.03525.
|
24 |
N. R. Baeth and D. Smertnig, Arithmetical invariants of local quaternion orders, Acta Arith. 186 (2018), no. 2, 143-177. https://doi.org/10.4064/aa170601-13-8
DOI
|
25 |
F. E. Brochero Martinez and S. Ribas, Extremal product-one free sequences in dihedral and dicyclic groups, Discrete Math. 341 (2018), no. 2, 570-578. https://doi.org/10.1016/j.disc.2017.09.024
DOI
|
26 |
F. E. Brochero Martinez and S. Ribas, The {1, s}-weighted Davenport constant in and an application in an inverse problem, submitted; https://arxiv.org/abs/1803.09705.
|
27 |
F. Chen and S. Savchev, Long minimal zero-sum sequences in the groups , Integers 14 (2014), Paper No. A23, 29 pp.
|
28 |
K. Cziszter, The Noether number of p-groups, J. Algebra Appl. 18 (2019), no. 4, 1950066, 14 pp. https://doi.org/10.1142/S021949881950066X
DOI
|
29 |
K. Cziszter and M. Domokos, The Noether number for the groups with a cyclic subgroup of index two, J. Algebra 399 (2014), 546-560. https://doi.org/10.1016/j.jalgebra.2013.09.044
DOI
|
30 |
K. Cziszter, M. Domokos, and A. Geroldinger, The interplay of invariant theory with multiplicative ideal theory and with arithmetic combinatorics, in Multiplicative ideal theory and factorization theory, 43-95, Springer Proc. Math. Stat., 170, Springer, 2016. https://doi.org/10.1007/978-3-319-38855-7_3
|
31 |
K. Cziszter, M. Domokos, and I. Szollosi, The Noether numbers and the Davenport constants of the groups of order less than 32, J. Algebra 510 (2018), 513-541. https://doi.org/10.1016/j.jalgebra.2018.02.040
DOI
|
32 |
Y. Fan, W. Gao, and Q. Zhong, On the Erdos-Ginzburg-Ziv constant of finite abelian groups of high rank, J. Number Theory 131 (2011), no. 10, 1864-1874. https://doi.org/10.1016/j.jnt.2011.02.017
DOI
|