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- Substructure abstract "In mathematical logic, an (induced) substructure or (induced) subalgebra is a structure whose domain is a subset of that of a bigger structure, and whose functions and relations are the traces of the functions and relations of the bigger structure. Some examples of subalgebras are subgroups, submonoids, subrings, subfields, subalgebras of algebras over a field, or induced subgraphs. Shifting the point of view, the larger structure is called an extension or a superstructure of its substructure.In model theory, the term \"submodel\" is often used as a synonym for substructure, especially when the context suggests a theory of which both structures are models.In the presence of relations (i.e. for structures such as ordered groups or graphs, whose signature is not functional) it may make sense to relax the conditions on a subalgebra so that the relations on a weak substructure (or weak subalgebra) are at most those induced from the bigger structure. Subgraphs are an example where the distinction matters, and the term \"subgraph\" does indeed refer to weak substructures. Ordered groups, on the other hand, have the special property that every substructure of an ordered group which is itself an ordered group, is an induced substructure.".
- Substructure wikiPageExternalLink graph.theory.
- Substructure wikiPageExternalLink ualg.html.
- Substructure wikiPageID "2057747".
- Substructure wikiPageLength "6125".
- Substructure wikiPageOutDegree "53".
- Substructure wikiPageRevisionID "702637344".
- Substructure wikiPageWikiLink Algebra_over_a_field.
- Substructure wikiPageWikiLink Algebraic_number.
- Substructure wikiPageWikiLink Algebraically_closed_field.
- Substructure wikiPageWikiLink Building.
- Substructure wikiPageWikiLink Cambridge_University_Press.
- Substructure wikiPageWikiLink Category:Model_theory.
- Substructure wikiPageWikiLink Category:Universal_algebra.
- Substructure wikiPageWikiLink Category_(mathematics).
- Substructure wikiPageWikiLink Civil_engineering.
- Substructure wikiPageWikiLink Complex_number.
- Substructure wikiPageWikiLink Concrete_category.
- Substructure wikiPageWikiLink Elementary_equivalence.
- Substructure wikiPageWikiLink Embedding.
- Substructure wikiPageWikiLink End_extension.
- Substructure wikiPageWikiLink Field_(mathematics).
- Substructure wikiPageWikiLink Field_extension.
- Substructure wikiPageWikiLink Glossary_of_graph_theory.
- Substructure wikiPageWikiLink Graph_(discrete_mathematics).
- Substructure wikiPageWikiLink Group_(mathematics).
- Substructure wikiPageWikiLink Löwenheim–Skolem_theorem.
- Substructure wikiPageWikiLink Mathematical_logic.
- Substructure wikiPageWikiLink Mathematics.
- Substructure wikiPageWikiLink Model_theory.
- Substructure wikiPageWikiLink Monoid.
- Substructure wikiPageWikiLink Ordered_field.
- Substructure wikiPageWikiLink Partially_ordered_group.
- Substructure wikiPageWikiLink Prime_model.
- Substructure wikiPageWikiLink Rational_number.
- Substructure wikiPageWikiLink Real_number.
- Substructure wikiPageWikiLink Signature_(logic).
- Substructure wikiPageWikiLink Springer_Science+Business_Media.
- Substructure wikiPageWikiLink Structure_(mathematical_logic).
- Substructure wikiPageWikiLink Subgroup.
- Substructure wikiPageWikiLink Subobject.
- Substructure wikiPageWikiLink Subring.
- Substructure wikiPageWikiLink Subset.
- Substructure wikiPageWikiLinkText "(induced) substructure".
- Substructure wikiPageWikiLinkText "Substructure".
- Substructure wikiPageWikiLinkText "extension".
- Substructure wikiPageWikiLinkText "subalgebra".
- Substructure wikiPageWikiLinkText "substructure".
- Substructure wikiPageUsesTemplate Template:About.
- Substructure wikiPageUsesTemplate Template:Citation.
- Substructure subject Category:Model_theory.
- Substructure subject Category:Universal_algebra.
- Substructure hypernym Structure.
- Substructure type Building.
- Substructure comment "In mathematical logic, an (induced) substructure or (induced) subalgebra is a structure whose domain is a subset of that of a bigger structure, and whose functions and relations are the traces of the functions and relations of the bigger structure. Some examples of subalgebras are subgroups, submonoids, subrings, subfields, subalgebras of algebras over a field, or induced subgraphs.".
- Substructure label "Substructure".
- Substructure sameAs Q859254.
- Substructure sameAs Subestrutura.
- Substructure sameAs m.02p5lhf.
- Substructure sameAs Delstruktur.
- Substructure sameAs Q859254.
- Substructure sameAs 子结构.
- Substructure wasDerivedFrom Substructure?oldid=702637344.
- Substructure isPrimaryTopicOf Substructure.