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the Assouad–Nagata dimension (sometimes simply Nagata dimension) is a notion of dimension for metric spaces, introduced by Jun-iti Nagata in 1958 and...

formula Nagata dimension or Assouad-Nagata dimension, a notion of dimension for metric spaces Nagata ring, an integral domain in algebra Nagata–Smirnov...

definitions of the asymptotic dimension and Assouad–Nagata dimension of a space: a space with asymptotic dimension n is n-dimensional "at large scales", and...

by Nagata in 1950 and by Smirnov in 1951, as well as the Assouad–Nagata dimension of a metric space, which he introduced in a 1958 article. Nagata became...

that is not catenary, and a commutative Noetherian ring of infinite dimension. Nagata's conjecture on curves concerns the minimum degree of a plane curve...

(R/r)n. The Assouad dimension of a metric space is always greater than or equal to its Assouad–Nagata dimension. The Assouad dimension of a metric space...

ideal has finite height. Nonetheless, Nagata gave an example of a Noetherian ring of infinite Krull dimension. A ring is called catenary if any inclusion...

in 1954). Then in 1959 Masayoshi Nagata found a counterexample to Hilbert's conjecture. The counterexample of Nagata is a suitably constructed ring of...

generated integral domain over it is Japanese, and is called a Nagata ring, named for Masayoshi Nagata, or a pseudo-geometric ring if it is Noetherian and universally...

one-dimensional noetherian domain. A consequence of the theorem is that if R is a Nagata ring, then every R-subalgebra of finite type is again a Nagata ring...

In mathematics, dimension theory is the study in terms of commutative algebra of the notion dimension of an algebraic variety (and by extension that of...

Masayoshi Nagata (1956, 1962, page 203 example 2), who found a 2-dimensional Noetherian local domain that is catenary but not universally catenary. Nagata's example...

They showed that regular local rings of dimension 3 are unique factorization domains, and Masayoshi Nagata (1958) had previously shown that this implies...

mathematics, the Chevalley–Iwahori–Nagata theorem states that if a linear algebraic group G is acting linearly on a finite-dimensional vector space V, then the...

varieties in dimension 3 and higher which are not projective. The first examples of non-projective complete varieties were given by Masayoshi Nagata and Heisuke...

irreducible of A is prime. A is a GCD domain satisfying (ACCP). The so-called Nagata criterion holds for an integral domain A satisfying (ACCP): Let S be a multiplicatively...

one can construct genuinely new examples of varieties in this way, but Nagata gave an example of such a new variety in the 1950s. For an algebraically...

Haboush's theorem to reductive groups over schemes. It follows from the work of Nagata (1963), Haboush, and Popov that the following conditions are equivalent...

125—126. Engelking, General Topology, Theorem 3.10.31 K.P. Hart, Jun-iti Nagata, J.E. Vaughan (editors), Encyclopedia of General Topology, Chapter d3 (by...

unramified. However Nagata (1955) gave an example of a 2-dimensional normal analytically ramified Noetherian local ring. Nagata also showed that a slightly...