# Nil geometry wikipedia

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. . For the type of algebra, see Nilpotent algebra. In mathematics, an element x of a ring R is called nilpotent if there exists some positive integer n, called the index (or sometimes the degree ), such that xn = 0. The term was introduced by Benjamin Peirce in the context of his work on the classification of algebras. Contents 1 Examples 2 Properties. リーマン幾何学（リーマンきかがく、英: Riemannian geometry ）とは、リーマン計量や擬リーマン計量と呼ばれる距離の概念を一般化した構造を持つ図形を研究する微分幾何学の分野である。 このような図形はリーマン多様体、擬リーマン多様体とよばれる。 ドイツの数学者ベルンハルト・リーマン. . . An element \$ a \$ of a ring or semi-group with zero \$ A \$ such that \$ a ^ {n} = 0 \$ for some natural number \$ n \$. The smallest such \$ n \$ is called the nilpotency index of \$ a \$. For example, in the residue ring modulo \$ p ^ {n} \$ ( under multiplication), where \$ p \$ is a prime number, the residue class of \$ p \$ is nilpotent of index \$ n \$; in. .

. . . . Nil algebra A power-associative (in particular, an associative) algebra (cf. Algebra with associative powers) in which every element is nilpotent (cf. Nilpotent element ). Special cases of nil algebras are nilpotent and locally nilpotent algebras (cf. Nilpotent algebra; Locally nilpotent algebra ). . . .

. . . Nil Geometry; S Solv Geometry; Spherical Geometry; Categories Categories: Add category; Cancel Save. Community content is available under CC-BY-SA unless otherwise noted. Advertisement. Explore properties. Fandom ... Hyperbolica Wiki is a FANDOM Games Community. View Mobile Site. . . An element \$ a \$ of a ring or semi-group with zero \$ A \$ such that \$ a ^ {n} = 0 \$ for some natural number \$ n \$. The smallest such \$ n \$ is called the nilpotency index of \$ a \$. For example, in the residue ring modulo \$ p ^ {n} \$ ( under multiplication), where \$ p \$ is a prime number, the residue class of \$ p \$ is nilpotent of index \$ n \$; in. .

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• In mathematics, a nilcurve is a pointed stable curve over a finite field with an indigenous bundle whose p-curvature is square nilpotent.Nilcurves were introduced by Mochizuki () as a central concept in his theory of p-adic Teichmüller theory.The nilcurves form a stack over the moduli stack of stable genus g curves with r marked points in characteristic p, of degree p 3g-3+r.