algebraic structure
Noun
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Noun
algebraic structure (plural algebraic structures)
- (algebra, universal algebra) Any one of the numerous types of mathematical object studied in algebra and especially in universal algebra.
- (more formally) A mathematical object comprising a carrier set (aka underlying set or domain), an optional scalar set, a set of operations (typically binary operations, but otherwise each of finite arity) and a set of identities (axioms) which the operations must satisfy.
- The definition of algebraic structure establishes a framework through which to compare otherwise very different abstract objects, and to study similarities and patterns made apparent by the definition.
- 1975, Ronald James Williams, Algebraic Structures Up to Homotopy, University of California, San Diego, page 16 ↗,
- In this chapter we propose a general means for describing algebraic structures, both strict and up to homotopy, and we apply the results of the preceding chapter to the study of these […] .
- 1995, George R. Kempf, Algebraic Structures, Bertelsmann (Vieweg), page 129 ↗,
- Thus the algebraic structures which we have been studying are part of category theory, but the important theorem is not generally categorical nonsense, although there are theorems in category theory which we will not study.
- (formal structure of a carrier set, operations and axioms) algebra (in the context of universal algebra), algebraic system, universal algebra
- French: structure algébrique
- German: algebraische Struktur
- Portuguese: estrutura algébrica
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.004