Semigroup

noun

noun ·Rare ·Advanced level

Definitions

Noun
  1. 1
    Any set for which there is a binary operation that is closed and associative.

    "If a semigroup S contains a zeroid, then every left zeroid is also a right zeroid, and vice versa, and the set K of all the zeroids of S is the kernel of S."

Example

More examples

"If a semigroup S contains a zeroid, then every left zeroid is also a right zeroid, and vice versa, and the set K of all the zeroids of S is the kernel of S."

Etymology

From semi- + group, reflecting the fact that not all the conditions required for a group are required for a semigroup. (Specifically, the requirements for the existence of identity and inverse elements are omitted.)

Related phrases

Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.