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Glite Dictionary
🔢 With nilpotent elements ⚗️ Not reacted 🔊 Not made simpler
nonreduced

nonreduced

9.9
A mathematical object like a ring or other structure that has elements whose powers become zero
  • adjective
  • /ˌnɒn.rɪˈdjuːst/
  • Specialized
translation icon : no reducido
  • In algebraic geometry, a nonreduced scheme has nilpotent elements that affect the structure of the space.

Examples

  • The ring is considered nonreduced because it contains nilpotent elements that influence its properties.

  • The important point is that this increase in S2 subjects is synonymous with the shift from reduced to nonreduced structures, which then motivated the shifts in case marking, clitic placement, use of se, and word order.

    Academic text (1995)

  • To better understand the concept, one must consider how a nonreduced object behaves differently from a reduced one.

Synonyms

unreduced
vsnonreduced
1 6.5

Still at the same size, amount, or strength as before

refers specifically to mathematical objects that contain nilpotent elements

Surface Forms

nonreduced positive

Morphology

nonreduced = reduced (semi-transparent) = non + reduce + ed

Formally 'non-' negates 'reduced', but the sense depends on the technical mathematical meaning of 'reduced' (no nilpotents), so it is not fully transparent to general learners.

Etymology

Nonreduced comes from the prefix non- meaning 'not' and reduced meaning 'made smaller or simpler'. In mathematics, a nonreduced object is one that was not simplified and still has hidden parts or extra layers, which is why it is called 'nonreduced'.