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LocalNR

Package of local nearrings

1.0.4

15 March 2024

Iryna Raievska
Email: raeirina@imath.kiev.ua
Homepage: https://www.imath.kiev.ua/~algebra/Raievska_I/
Address:
Institute of Mathematics
National Academy of Sciences of Ukraine
01024 Ukraine, Kyiv, 3, Tereshchenkivska st.

Maryna Raievska
Email: raemarina@imath.kiev.ua
Homepage: https://www.imath.kiev.ua/~algebra/Raievska_M/
Address:
Institute of Mathematics
National Academy of Sciences of Ukraine
01024 Ukraine, Kyiv, 3, Tereshchenkivska st.

Yaroslav Sysak
Email: sysak@imath.kiev.ua
Homepage: https://www.imath.kiev.ua/~algebra/Sysak/
Address:
Institute of Mathematics
National Academy of Sciences of Ukraine
01024 Ukraine, Kyiv, 3, Tereshchenkivska st.

Contents

1 Local nearrings

1.1 The local nearrings library

  1.1-1 TheAdditiveGroupsOfLibraryOfLNRsOfOrder
  1.1-2 TheLibraryOfLNRsOnGroup
  1.1-3 LocalNearRing
  1.1-4 AllLocalNearRings
  1.1-5 IsAdditiveGroupOfLibraryOfLNRs
  1.1-6 InfoLocalNearRing

2.1 Group functions

  2.1-1 IsMinimalNonAbelianGroup
  2.1-2 IsMetacyclicPGroup
  2.1-3 EndoOrbitsOfGroup
  2.1-4 IsEndoCyclicGroup

2.2 Nearring functions

  2.2-1 UnitsOfNearRing
  2.2-2 IsLocalNearRing
  2.2-3 IsLocalRing
  2.2-4 NearRingNonUnits
  2.2-5 SubNearRingByGenerators
  2.2-6 NonUnitsAsAdditiveSubgroup
  2.2-7 NonUnitsAsNearRingIdeal
  2.2-8 MultiplicativeSemigroupOfNearRing
  2.2-9 NonUnitsAsMultiplicativeSemigroup
  2.2-10 IsOneGeneratedNearRing
  2.2-11 AutomorphismsAssociatedWithNearRingUnits
  2.2-12 EndomorphismsAssociatedWithNearRingElements
  2.2-13 SemidirectProductAssociatedWithNearRing
  2.2-14 IsCircleSubgroupOfNearRing
  2.2-15 FactorizedGroupAssociatedWithCircleSubgroupOfNearRing
  2.2-16 ConstantPartOfNearRing
  2.2-17 ZeroSymmetricPartOfNearRing
  2.2-18 GroupOfUnitsAsGroupOfAutomorphisms
  2.2-19 IsDistributiveElementOfNearRing
  2.2-20 IsSemiDistributiveNearRing
  2.2-21 IsNearRingWithIdentity
  2.2-22 IsSubNearRing

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