Abstract
A cover of a finite ring is a collection of proper subrings of such that . If such a collection exists, then is called coverable, and the covering number of is the cardinality of the smallest possible cover. We investigate covering numbers for rings of upper triangular matrices with entries from a finite field. Let be the field with elements and let be the ring of upper triangular matrices with entries from . We prove that if , then has covering number , that has covering number 4, and that when is prime, has covering number for all .
Citation
Merrick Cai. Nicholas J. Werner. "Covering numbers of upper triangular matrix rings over finite fields." Involve 12 (6) 1005 - 1013, 2019. https://doi.org/10.2140/involve.2019.12.1005
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