SONATA

The use of computers in near-ring theory This paper describes the facilities available in a computer system developed by the authors at the University of Linz, Austria, for investigating near-rings. The use of computers to investigate near-rings goes back a long way to the mid 1960s and J. R. Clay. This report opens up a new era in this field by providing a system SONATA (System Of Near-rings And Their Applications) based on GAP, the well known powerful program for groups. A description of the methods used is given. The amount of information that can be obtained is very substantial and can deal with very large near-rings, in some cases up to 10^50 elements in size. Several examples of possible use are described. This is a very useful major achievement. Computer algebra system (CAS).


References in zbMATH (referenced in 15 articles , 2 standard articles )

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  1. Horváth, Gábor: The complexity of the equivalence and equation solvability problems over meta-abelian groups (2015)
  2. Peterson, Gary L.; Scott, Stuart D.: Units of compatible nearrings. III. (2013)
  3. Hedtke, Ivo; Murthy, Sandeep: Search and test algorithms for triple product property triples. (2012)
  4. Benini, Anna; Frigeri, Achille; Morini, Fiorenza: Codes and combinatorial structures from circular planar nearrings (2011)
  5. Peterson, Gary L.: Compatible extensions of nearrings. (2010)
  6. Wendt, G.: Minimal left ideals of near-rings. (2010)
  7. Peterson, Gary L.: Some problems in the theory of nearring modules. (2009)
  8. Aichinger, E.; Mayr, P.: Polynomial clones on groups of order $pq$ (2007)
  9. Aichinger, Erhard: The near-ring of congruence-preserving functions on an expanded group. (2006)
  10. Mayr, Peter: The polynomial functions on Frobenius complements. (2006)
  11. Benini, A.; Morini, F.: Partially balanced incomplete block designs from weakly divisible nearrings (2005)
  12. Kowol, Gerhard: Polynomial functions over groups: from algebraically closed groups to endomorphism near-rings. (2004)
  13. Mayr, Peter; Morini, Fiorenza: Nearrings whose set of $N$-subgroups is linearly ordered. (2002)
  14. Aichinger, Erhard: On the maximal ideals of non-zero-symmetric near-rings and of composition algebras of polynomial functions on $\Omega$-groups (2001)
  15. Aichinger, Erhard; Ecker, Jürgen; Nöbauer, Christof: The use of computers in near-ring theory (2001)