Report Number: CS-TR-72-258
Institution: Stanford University, Department of Computer Science
Title: Some basic machine algorithms for integral order computations.
Author: Brown, Harold
Date: February 1972
Abstract: Three machine implemented algorithms for computing with integral orders are described. The algorithms are: 1. For an integral order R given in terms of its left regular representation relative to any basis, compute the nil radical J(R) and a left regular representation of R/J(R). 2. For a semisimple order R given in terms of its left regular representation relative to any basis, compute a new basis for R and the associated left regular representation of R such that the first basis element of the transformed basis is an integral multiple of the identity element in Q \$\bigotimes\$ R. 3. Relative to any fixed Z -basis for R, compute a unique canonical form for any given finitely generated Z -submodule of Q \$\bigotimes\$ R described in terms of that basis.
http://i.stanford.edu/pub/cstr/reports/cs/tr/72/258/CS-TR-72-258.pdf