Noetherianadj.

Brit.

/nəʊˈθɪərɪən/, U.S.

/noʊˈθɪriən/

Forms: also with lower-case initial.

Origin: From a proper name, combined with an English element. Etymons: proper name Noether , -ian suffix.

Etymology: < Noether, the family name of two German mathematicians, Max Noether (1844–1921), and his daughter Emmy (Amalie) Noether (1882–1935) + -ian suffix.

Mathematics.

1. Of, relating to, or arising from the work of Max or (esp. in later use) Emmy Noether.Both Max and Emmy Noether made foundational contributions to the field of algebraic geometry. Emmy also carried out significant work in the fields of abstract algebra and theoretical physics.

ΚΠ

1908 Amer. Jrnl. Math. 30 69 The modulus (u, v) will comprise in all 16 Noetherian conditions.

1941 Amer. Jrnl. Math. 63 681 Our decomposition theorem..is distinctly Noetherian in form, so general, even, as to unite the theory of algebraic difference equations with the theory of numbers.

1981 Conc. Dict. Sci. Biogr. 510/2 The equation..can be expressed in the form AΦ + BΨ = 0..if and only if certain conditions (today called ‘Noetherian conditions’) are satisfied.

2018 Symmetry 10 No. 744 4 The ease of determination of a Noetherian integral once the Noether symmetry is known is in contrast to the situation for the determination of first integrals in the case of Lie symmetries of differential equations.

2. spec. Designating a ring in which there exists no infinitely growing sequence of ideals such that each ideal is a subset of the next in sequence. Also: designating a module in which there exists no infinitely growing sequence of submodules such that each is a subset of its successor. left (also right) Noetherian n. designating a ring in which there exists no infinitely growing sequence of left (or right) ideals such that each is a subset of its successor.Such rings were first described by Emmy Noether in 1921 ( Math. Ann. 83 24–66).

ΚΠ

1943 Ann. Math. 44 690 A ring D is said to be Noetherian if the maximal condition holds for the ideals in D.

1966 Math. Rev. 31 33/2 The emphasis is on existence theorems and schemas on a complete Noetherian local ring.

1979 Proc. London Math. Soc. 38 217 Suppose that S is an integrally closed Noetherian domain contained in the centre of a prime polycentral ring R.

1990 Glasgow Math. Jrnl. 32 389 It was shown..that a generalized V-module (GV-module) has Krull dimension if and only if it is noetherian.

1990 Q. Jrnl. Math. 41 1 Let R be a right and left Noetherian, right and left fully bounded ring—an FBN ring, for short.

This is a new entry (OED Third Edition, December 2003; most recently modified version published online March 2022).

单词	noetherian
释义	Noetherianadj. Brit. /nəʊˈθɪərɪən/, U.S. /noʊˈθɪriən/ Forms: also with lower-case initial. Origin: From a proper name, combined with an English element. Etymons: proper name Noether , -ian suffix. Etymology: < Noether, the family name of two German mathematicians, Max Noether (1844–1921), and his daughter Emmy (Amalie) Noether (1882–1935) + -ian suffix. Mathematics. 1. Of, relating to, or arising from the work of Max or (esp. in later use) Emmy Noether.Both Max and Emmy Noether made foundational contributions to the field of algebraic geometry. Emmy also carried out significant work in the fields of abstract algebra and theoretical physics. ΚΠ 1908 Amer. Jrnl. Math. 30 69 The modulus (u, v) will comprise in all 16 Noetherian conditions. 1941 Amer. Jrnl. Math. 63 681 Our decomposition theorem..is distinctly Noetherian in form, so general, even, as to unite the theory of algebraic difference equations with the theory of numbers. 1981 Conc. Dict. Sci. Biogr. 510/2 The equation..can be expressed in the form AΦ + BΨ = 0..if and only if certain conditions (today called ‘Noetherian conditions’) are satisfied. 2018 Symmetry 10 No. 744 4 The ease of determination of a Noetherian integral once the Noether symmetry is known is in contrast to the situation for the determination of first integrals in the case of Lie symmetries of differential equations. 2. spec. Designating a ring in which there exists no infinitely growing sequence of ideals such that each ideal is a subset of the next in sequence. Also: designating a module in which there exists no infinitely growing sequence of submodules such that each is a subset of its successor. left (also right) Noetherian n. designating a ring in which there exists no infinitely growing sequence of left (or right) ideals such that each is a subset of its successor.Such rings were first described by Emmy Noether in 1921 ( Math. Ann. 83 24–66). ΚΠ 1943 Ann. Math. 44 690 A ring D is said to be Noetherian if the maximal condition holds for the ideals in D. 1966 Math. Rev. 31 33/2 The emphasis is on existence theorems and schemas on a complete Noetherian local ring. 1979 Proc. London Math. Soc. 38 217 Suppose that S is an integrally closed Noetherian domain contained in the centre of a prime polycentral ring R. 1990 Glasgow Math. Jrnl. 32 389 It was shown..that a generalized V-module (GV-module) has Krull dimension if and only if it is noetherian. 1990 Q. Jrnl. Math. 41 1 Let R be a right and left Noetherian, right and left fully bounded ring—an FBN ring, for short. This is a new entry (OED Third Edition, December 2003; most recently modified version published online March 2022). < adj.1908
随便看	independent television authority independent variable independent witness independented independentish independentism independently independents independing indeplorable indeposable indepravate indeprecable indeprehensible indeprivability indeprivable indepth inderborite inderite inderkins indescribabilities indescribability indescribable indescribableness indescribablenesses