2011/04/25 by C. Bekh-Ochir, Chuluun Bekh-Ochir, Bekh-Ochir, Chuluun +3
Engineering · Mathematics · #16R10 #Advanced Topics in Algebra #FOS: Mathematics #Photonic and Optical Devices #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #msc:16R10
paper · pdf · doi:10.48550/arxiv.1104.4755
arxiv created 2011/04/25 · openalex publication_date 2011/04/25 · arxiv updated 2011/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In earlier work, it was established that for any finite field k, the free associative k-algebra on one generator x, denoted by k[x]0, had infinitely many maximal T-spaces, but exactly two maximal ideals (each of which is a maximal T-space). However, aside from these two T-ideals, no examples of maximal T-spaces of k[c]0 have been identified. This paper presents, for each finite field k, an infinite sequence of proper T-spaces of k[x]0 (no one of which is a T-ideal), each of finite codimension, and for each one, both a linear basis for the T-space itself and a linear basis for a complementary linear subspace are provided. Morever, it is proven that the first T-space in the sequence is a maximal T-space of k[x]0, thereby providing the first example of a maximal T-space of k[x]0 that is not a maximal T-ideal.