OKlibrary  0.2.1.6
BasicNotions.hpp File Reference

Plans about the general notions for ringframes. More...

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Detailed Description

Plans about the general notions for ringframes.

Todo:
Notions and abbreviations for ringframes
  • Most general a "ringframe" [R,+,*].
  • A "ringframe" : "rngfrm"
  • A "prering" : "prrng"
  • A "semiring" : "srng"
  • A "nearring" : "nerrng"
  • A "ring" : "rng"
  • A "field" : "fld"
  • A "skewfield" : "skfld"
  • Commutative : "c"
  • Associative : "a"
  • "Pseudo" : "p"
  • "Null" : "n"
  • "Unit" : "u"
  • "left" : "l"
  • "right" : "r"
  • "additively" : "add"
  • "multiplicately" : "mul"
  • For a ring we can always add the additive inversion. Perhaps we also have the concept of a "partial inversion", which returns false in case of non-invertibility (or another given default-value); this would allow to have also multiplicative inversions.
  • We need to have "partial groupoids" and "partial ringframes", etc.
Todo:
Notions and abbreviations for modules and generalisations
  • Most general is a "moduleframe", which is the operation of a ringframe on a groupod.
  • A "moduleframe" : "mdlfrm"
  • A "premodule" : "prmdl" (the operation of a prering on a groupoid)
  • A "semimodule" : "smdl" (the operation of a semiring on a commutative monoid)
  • A "module" : "mdl" (the operation of a ring on an abelian group)
  • A "vectorspace" : "vcsp" (the operation of a (skew)field on an abelian group)

Definition in file BasicNotions.hpp.