Arithmetical invariants of local quaternion orders
Tom 186 / 2018
Acta Arithmetica 186 (2018), 143-177
MSC: 16H10, 11R27, 11S45.
DOI: 10.4064/aa170601-13-8
Opublikowany online: 14 September 2018
Streszczenie
Let be a DVR, let K be its quotient field, and let R be a D-order in a quaternion algebra A over K. The elasticity of R^\bullet is \rho(R^\bullet) = \sup\{k/l : u_1\cdots u_k = v_1 \cdots v_l with u_i, v_j atoms of R^\bullet and k, l \ge 1\} and is one of the basic arithmetical invariants that is studied in factorization theory. We characterize finiteness of \rho(R^\bullet) and show that the set of distances \Delta(R^\bullet) and all catenary degrees \mathsf c_{\mathsf d}(R^\bullet) are finite. In the setting of non-commutative orders in central simple algebras, such results have only been known for hereditary orders and for a few individual examples.
