different between algebraic vs semiring

English

Etymology

algebra +? -ic

Pronunciation

• IPA^(key): /?æld???b?e??k/
• Rhymes: -e??k

Adjective

algebraic (comparative more algebraic, superlative most algebraic)

1. Of, or relating to, algebra.
2. (mathematics, of an expression, equation, or function) Containing only numbers, letters, and arithmetic operators.
3. (algebra, number theory, of a number) Which is a root of some polynomial whose coefficients are rational.
4. (algebra, of a field) Whose every element is a root of some polynomial whose coefficients are rational.
5. (chess, of notation) Describing squares by file (referred to in intrinsic order rather than by the piece starting on that file) and rank, both with reference to a fixed point rather than a player-dependent perspective.

Antonyms

• (that is the root of some polynomial): transcendental
• (whose every element is the root of some polynomial): transcendental

Hyponyms

• (that is the root of some polynomial): quadratic number

Derived terms

• algebraic function
• algebraic equation
• algebraical
• algebraically
• algebraicize
• (of or relating to algebra):
  • algebraic geometry
  • algebraic number theory
  • algebraic structure
• (that is a root of some polynomial):
  • algebraic integer
  • algebraic number

Translations

Catalan

Pronunciation

• (Balearic, Central) IPA^(key): /??.???b?ajk/
• (Valencian) IPA^(key): /a?.d??e?b?ajk/

Adjective

algebraic (feminine algebraica, masculine plural algebraics, feminine plural algebraiques)

1. algebraic

   Synonym: algèbric

Derived terms

• algebraicament

Related terms

• àlgebra

Further reading

• “algebraic” in Diccionari de la llengua catalana, segona edició, Institut d’Estudis Catalans.

English

Etymology

semi- +? ring

Noun

semiring (plural semirings)

1. (algebra) An algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse.
2. (anatomy) One of the incomplete rings of the upper part of the bronchial tubes of most birds, forming an essential part of the syrinx of songbirds.

Hyponyms

• (algebra): ring

Anagrams

• remising