Title: Modules, Monoids, and Factorizations
Participants:
Alfred Geroldinger (PI, 1.10.2023 - ...)
Zahra Nazemian (Post doc, 1.6.2023 - ... )
Andreas Reinhart (Post doc, 1.8.2024 - 31. 7.2026)
Daniel Smertnig (PI, 1.6.2023 - 30.9. 2023)
Publications Funded by this project:
1) A. Reinhart and G. Ulucak: Multiplicative Lattices with Absorbing Factorization, Communications in Algebra, 2025, vol 53, https://doi.org/10.1080/00927872.2025.2505079 (PDF)
2) Zahra Nazemian, Realization of monoids with countable sum, Journal of Algebra and Its Applications, 2026, https://doi.org/10.1142/S0219498826430012, (PDF), https://arxiv.org/abs/2404.15769
3) Z. Nazemian and D. Smertnig, A monoid-theoretical approach to infinite direct sum decompositions of modules, 2024, (PDF), https://arxiv.org/pdf/2401.08203.pdf
4) J. Bell, D. Smertnig and H. Tamm, Duality of lattices associated to left and right quotients, 2023.
Proceedings of the 16th International Conference on Automata and Formal Languages, AFL 2023, Eger, Hungary, September 5-7, 2023, EPTCS, vol. 386, 2023, pp. 35–50.
https://arxiv.org/abs/2306.02491v2
5) V. Fadinger, S. Frisch, S. Nakato, D. Smertnig, D. Windisch, Primes and absolutely or non-absolutely
irreducible elements in atomic domains, Communications in Algebra, https://doi.org/10.1080/00927872.2025.2586234
6) W. Imrich, I. Klep, D. Smertnig, Monoid algebras and graph products, Art of Discrete and Applied
Mathematics, 2025. (Vol. 8 No. 1), Article P1.11.
https://doi.org/10.26493/2590-9770.1816.e85
7) Ideal Theory of Commutative Rings and Monoids, Franz Halter-Koch, Alfred Geroldinger, and Andreas Reinhart,
Springer Lecture Notes in Mathematics, Mathematics, vol. 2368, (2025)
https://link.springer.com/book/9783031888779
8) H. Huang, Z. Nazemian, Y. Wang, and J. J. Zhang, Relative Cancellation, Proceedings of the American
Mathematical Society, 2025, https://doi.org/10.1090/proc/17583,
https://pubs.ams.org/PROC/2026-154-08/S0002-9939-2026-17583-4
9) Z. Nazemian and M. K. Demir, Aut-stable subspaces of Grassmann algebras, Communications in Algebra, 2026,
https://doi.org/10.1080/00927872.2026.2631169 (PDF)
10) Submitted: H. Huang, Z. Nazemian, X. Tang, X. Wang, Y. Wang, and J. J. Zhang, Relative Dixmier Property for
Poisson Algebras, 2026, https://arxiv.org/pdf/2601.18249