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Algebraic Structures
Algebraic Structures
foundations +26 more results +18 more equations depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) step_from (declared) definition 4.1: Cartesian product 4.1 Cartesian product definition 4.2: Binary operation 4.2 Binary operation definition 4.3: Algebraic structure 4.3 Algebraic struct… definition 4.4: Internal binary operation; magma 4.4 Internal binary… definition 4.6: Associativity 4.6 Associativity definition 4.8: Commutativity; abelian structure 4.8 Commutativity; a… definition 4.9: Neutral element 4.9 Neutral element definition 4.11: Inverse element 4.11 Inverse element definition 4.12: Substructure 4.12 Substructure notation 4.13: The opposite map is not the inverse map 4.13 The opposite map… definition 4.15: Kernel 4.15 Kernel definition 4.16: Image 4.16 Image definition 4.18: Semigroup 4.18 Semigroup proposition 4.10: Uniqueness of the neutral element 4.10 Uniqueness of th… proposition 4.14: Maps into a group form a group 4.14 Maps into a grou… proposition 4.17: Trivial kernel of a homomorphism 4.17 Trivial kernel o… proposition 4.23: Uniqueness of the inverse element 4.23 Uniqueness of th… proposition 4.24: Inverse of the neutral element 4.24 Inverse of the n… proposition 4.25: Neutral element equal to a product 4.25 Neutral element… proposition 4.26: Involution of the inverse 4.26 Involution of th… proposition 4.27: Inverse of a product 4.27 Inverse of a pro… proposition 4.38: prop:alg-nZ-subgroup 4.38 proposition proposition 4.40: prop:alg-congruence-equiv 4.40 proposition proposition 4.41: prop:alg-zn-group 4.41 proposition proposition 4.42: When the homomorphisms form a group 4.42 When the homomor… proposition 4.46: Image of the neutral element 4.46 Image of the neu… equation 4.6: eq:alg-opposite-map eq. (4.6) equation 4.25: eq:alg-hom-inverse eq. (4.25) equation 4.30: eq:alg-s3-elements eq. (4.30) equation 4.35: eq:alg-coset-neutral eq. (4.35) equation 4.36: eq:alg-norm2 eq. (4.36) equation 4.37: eq:alg-norm3 eq. (4.37) equation 4.38: eq:alg-coset-product eq. (4.38) The chain of Algebraic Structures: 33 of 77 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.