Prime groupoid graded rings with applications to partial skew groupoid rings

References

• Bagio, D., Flores, D., Paques, A. (2010). Partial actions of ordered groupoids on rings. J. Algebra Appl. 9(3):501–517. DOI: 10.1142/S021949881000404X.
   Web of Science ®Google Scholar
• Bagio, D., Gonçalves, D., Moreira, P. S. E., Öinert, J. (2024). The ideal structure of partial skew groupoid rings with applications to topological dynamics and ultragraph algebras. Forum Math. DOI: 10.1515/forum-2023-0117.(To appear).
   Web of Science ®Google Scholar
• Bagio, D., Paques, A. (2012). Partial groupoid actions: globalization, Morita theory, and Galois theory. Commun. Algebra 40(10):3658–3678. DOI: 10.1080/00927872.2011.592889.
   Web of Science ®Google Scholar
• Bagio, D., Paques, A., Pinedo, H. (2021). On partial skew groupoid rings. Int. J. Algebra Comput. 31(1):1–7. DOI: 10.1142/S0218196721500016.
   Google Scholar
• Bagio, D., Sant’Ana, A., Tamusiunas, T. (2022). Galois correspondence for group-type partial actions of groupoids. Bull. Belg. Math. Soc. Simon Stevin. 28(5):745–767. DOI: 10.36045/j.bbms.210807.
   Web of Science ®Google Scholar
• Caenepeel, S., De Groot, E. (2007). Galois theory for weak Hopf algebras. Rev. Roumaine Math. Pures Appl. 52(2):151–176.
   Google Scholar
• Connell, I. (1963). On the group ring. Canad. J. Math. 15:650–685. DOI: 10.4153/CJM-1963-067-0.
   Web of Science ®Google Scholar
• Gonçalves, D., Yoneda, G. (2016). Free path groupoid grading on Leavitt path algebras. Int. J. Algebra Comput. 26(6):1217–1235. DOI: 10.1142/S021819671650051X.
   Web of Science ®Google Scholar
• Lännström, D., Lundström, P., Öinert, J., Wagner, S. (2021). Prime group graded rings with applications to partial crossed products and Leavitt path algebras. arXiv preprint arXiv:2105.09224.
   Google Scholar
• Lännström, D., Öinert, J. (2022). Graded von Neumann regularity of rings graded by semigroups. Beiträge zur Algebra und Geometrie/Contributions to Algebra and Geometry. DOI: 10.1007/s13366-022-00673-9.(To appear).
   Web of Science ®Google Scholar
• Lundström, P. (2004). The category of groupoid graded modules. Colloq. Math. 100(2):195–211. DOI: 10.4064/cm100-2-4.
   Google Scholar
• Lundström, P. (2006). Strongly groupoid graded rings and cohomology. Colloq. Math. 106(1):1–13. DOI: 10.4064/cm106-1-1.
   Google Scholar
• Munn, W. D. (1990). On contracted semigroup rings. Proc. Roy. Soc. Edinburgh Sect. A 115(1–2):109–117. DOI: 10.1017/S0308210500024604.
   Google Scholar
• Munn, W. D. (2000). Rings graded by bisimple inverse semigroups. Proc. Roy. Soc. Edinburgh Sect. A 130(3):603–609. DOI: 10.1017/S0308210500000329.
   Google Scholar
• Nystedt, P. (2019). A survey of s-unital and locally unital rings. Rev. Integr. Temas Mat. 37(2):251–260. DOI: 10.18273/revint.v37n2-2019003.
   Google Scholar
• Nystedt, P., Öinert, J. (2020). Group gradations on Leavitt path algebras. J. Algebra Appl. 19(9):2050165. DOI: 10.1142/S0219498820501650.
   Web of Science ®Google Scholar
• Nystedt, P., Öinert, J., Pinedo, H. (2018). Epsilon-strongly graded rings, separability and semisimplicity. J. Algebra 514:1–24. DOI: 10.1016/j.jalgebra.2018.08.002.
   Web of Science ®Google Scholar
• Nystedt, P., Öinert, J., Pinedo, H. (2020). Epsilon-strongly groupoid-graded rings, the Picard inverse category and cohomology. Glasg. Math. J. 62(1):233–259. DOI: 10.1017/S0017089519000065.
   Web of Science ®Google Scholar
• Öinert, J. Units, zero-divisors and idempotents in rings graded by torsion-free groups. J. Group Theory, to appear.
   Web of Science ®Google Scholar
• Öinert, J., Lundström, P. (2010). Commutativity and ideals in category crossed products. Proc. Est. Acad. Sci. 59(4):338–346. DOI: 10.3176/proc.2010.4.13.
   Web of Science ®Google Scholar
• Öinert, J., Lundström, P. (2012). The ideal intersection property for groupoid graded rings. Commun. Algebra 40(5):1860–1871. DOI: 10.1080/00927872.2011.559181.
   Web of Science ®Google Scholar
• Passman, D. S. (1984). Infinite crossed products and group-graded rings. Trans. Amer. Math. Soc. 284(2):707–727. DOI: 10.1090/S0002-9947-1984-0743740-2.
   Web of Science ®Google Scholar
• Steinberg, B. (2010). A groupoid approach to discrete inverse semigroup algebras. Adv. Math. 223(2):689–727. DOI: 10.1016/j.aim.2009.09.001.
   Web of Science ®Google Scholar
• Steinberg, B. (2019). Prime étale groupoid algebras with applications to inverse semigroup and Leavitt path algebras. J. Pure Appl. Algebra 223(6):2474–2488. DOI: 10.1016/j.jpaa.2018.09.003.
   Web of Science ®Google Scholar
• Tominaga, H. (1976). On s-unital rings. Math. J. Okayama univ. 18:117–134.
   Google Scholar