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 21 articles , 3 standard articles )

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  1. Földvári, Attila; Horváth, Gábor: The complexity of the equation solvability and equivalence problems over finite groups (2020)
  2. Farag, Mark; Tucci, Ralph: BZS rings (2019)
  3. Maxson, C. J.; Saxinger, Frederik: Rings of congruence preserving functions (2018)
  4. Aichinger, Erhard; Yatchak, Rika: SONATA: a GAP tool for nearring computations (2016)
  5. Kuncham, Syam Prasad; Jagadeesha, B.; Kedukodi, Babushri Srinivas: Interval valued L-fuzzy cosets of nearrings and isomorphism theorems (2016)
  6. Horváth, Gábor: The complexity of the equivalence and equation solvability problems over meta-abelian groups (2015)
  7. Lavoura, L.; Ludl, P. O.: Residual (\mathbbZ_2\times\mathbbZ_2) symmetries and lepton mixing (2014)
  8. Peterson, Gary L.; Scott, Stuart D.: Units of compatible nearrings. III. (2013)
  9. Hedtke, Ivo; Murthy, Sandeep: Search and test algorithms for triple product property triples. (2012)
  10. Benini, Anna; Frigeri, Achille; Morini, Fiorenza: Codes and combinatorial structures from circular planar nearrings (2011)
  11. Peterson, Gary L.: Compatible extensions of nearrings. (2010)
  12. Wendt, G.: Minimal left ideals of near-rings. (2010)
  13. Peterson, Gary L.: Some problems in the theory of nearring modules. (2009)
  14. Aichinger, E.; Mayr, P.: Polynomial clones on groups of order (pq) (2007)
  15. Aichinger, Erhard: The near-ring of congruence-preserving functions on an expanded group. (2006)
  16. Mayr, Peter: The polynomial functions on Frobenius complements. (2006)
  17. Benini, A.; Morini, F.: Partially balanced incomplete block designs from weakly divisible nearrings (2005)
  18. Kowol, Gerhard: Polynomial functions over groups: from algebraically closed groups to endomorphism near-rings. (2004)
  19. Mayr, Peter; Morini, Fiorenza: Nearrings whose set of (N)-subgroups is linearly ordered. (2002)
  20. Aichinger, Erhard: On the maximal ideals of non-zero-symmetric near-rings and of composition algebras of polynomial functions on (\Omega)-groups (2001)

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