injectiveadj.

/ɪnˈdʒɛktɪv/

Etymology: < inject v. (or Latin inject- participial stem) + -ive suffix.

Mathematics.

Of the nature of or pertaining to an injection (sense 5).

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > transformation > [adjective] > having specific correspondence

orthogonal1852

permutational1888

isomorphic1892

birational1894

unary1931

homomorphic1935

symplectic1939

involutory1941

injective1952

monomorphic1958

bijective1962

surjective1964

1952 S. Eilenberg & N. E. Steenrod Found. Algebraic Topol. i. 8 A set of homomorphisms i_α: G_α → G, α = 1,…, n, determine a homomorphism i:Σⁿ_{α = 1}G_α → G... If i is an isomorphism of ΣG_α onto G, then the set {i_α} is called an injective representation of G as a direct sum.

1965 J. J. Rotman Theory of Groups ix. 184 (heading) The injective property.

1966 Sze-Tsen Hu Introd. Gen. Topol. i. 8 A function f: X → Y is said to be one-to-one or injective iff, for every point y ∈ Y, the inverse image f⁻¹(y) is either empty or a singleton.

This entry has not yet been fully updated (first published 1976; most recently modified version published online June 2018).

单词	injective
释义	injectiveadj. /ɪnˈdʒɛktɪv/ Etymology: < inject v. (or Latin inject- participial stem) + -ive suffix. Mathematics. Of the nature of or pertaining to an injection (sense 5). ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [adjective] > having specific correspondence orthogonal1852 permutational1888 isomorphic1892 birational1894 unary1931 homomorphic1935 symplectic1939 involutory1941 injective1952 monomorphic1958 bijective1962 surjective1964 1952 S. Eilenberg & N. E. Steenrod Found. Algebraic Topol. i. 8 A set of homomorphisms i_α: G_α → G, α = 1,…, n, determine a homomorphism i:Σⁿ_{α = 1}G_α → G... If i is an isomorphism of ΣG_α onto G, then the set {i_α} is called an injective representation of G as a direct sum. 1965 J. J. Rotman Theory of Groups ix. 184 (heading) The injective property. 1966 Sze-Tsen Hu Introd. Gen. Topol. i. 8 A function f: X → Y is said to be one-to-one or injective iff, for every point y ∈ Y, the inverse image f⁻¹(y) is either empty or a singleton. This entry has not yet been fully updated (first published 1976; most recently modified version published online June 2018). < adj.1952
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