Quotients of skew polynomial rings: new constructions of division algebras and MRD codes Lobillo Borrero, Francisco Javier Santonastaso, Paolo Sheekey, John Skew polynomial rings Division algebra Semifield We achieve new results on skew polynomial rings and their quotients, including the first explicit example of a skew polynomial ring where the ratio of the degree of a skew polynomial to the degree of its bound is not extremal. These methods lead to the construction of new (not necessarily associative) division algebras and maximum rank distance (MRD) codes over both finite and infinite division rings. In particular, we construct new non-associative division algebras whose right nucleus is a central simple algebra having degree greater than 1. Over finite fields, we obtain new semifields and MRD codes for infinitely many choices of parameters. These families extend and contain many of the best previously known constructions. 2025-12-05T11:48:22Z 2025-12-05T11:48:22Z 2025-12-04 journal article F.J. Lobillo et al; Quotients of skew polynomial rings: new constructions of division algebras and MRD codes, J. Algebra (2025), doi: https://doi.org/10.1016/j.jalgebra.2025.11.024 https://hdl.handle.net/10481/108623 10.1016/j.jalgebra.2025.11.024 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Elsevier