indecomposable

An indecomposable substance remains unchanged in the chemical reaction.

Definition

1. Adjective:
   • Not able to be decomposed: "indecomposable" describes something that cannot be broken down into simpler parts or elements.
   • In mathematics: Refers to an object (such as a number, polynomial, or module) that cannot be expressed as a product or sum of two or more nontrivial components.

Usage Examples

• (It could not be broken down into simpler substances.)
• (It cannot be split into smaller group components.)
• (It cannot be divided into parts.)

Advanced Usage

• "Indecomposable module": In ring theory, a module that cannot be written as a direct sum of two nonzero submodules.

  • The study of indecomposable modules is central to understanding the structure of rings. (These modules are building blocks of module theory.)

• "Indecomposable continuum": In topology, a continuum that cannot be expressed as the union of two proper subcontinua.

  • The pseudo-arc is a famous example of an indecomposable continuum in topology. (It is a connected space that cannot be split into two smaller connected subsets.)

Variants and Related Words

• Indecomposability (noun): the quality of being indecomposable.
  • The indecomposability of this polynomial was proven by the mathematician. (Its inability to be factored.)
• Decomposable (adj): able to be broken down (antonym).
  • Unlike the indecomposable compound, this one is easily decomposable. (It can be broken down.)

Synonyms

• Irreducible: not reducible to a simpler form.
• Unbreakable: not capable of being broken or separated.
• Indivisible: cannot be divided into parts.

Antonyms

• Decomposable: capable of being broken down.
• Reducible: able to be simplified or broken into parts.

Related Idioms