In mathematics, a von Neumann regular ring is a ring R (associative, with 1, not necessarily commutative) such that for every element a in R there exists...

a von Neumann regular ring. (The von Neumann algebra itself is in general not von Neumann regular.) The relationship between commutative von Neumann algebras...

von Neumann regular rings. For Noetherian local rings, there is the following chain of inclusions: Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein...

Neumann conjecture Von Neumann entropy Von Neumann machine (disambiguation) Von Neumann neighborhood Von Neumann regular ring Von Neumann universe This disambiguation...

Neumann neighborhood von Neumann ordinal von Neumann paradox von Neumann probe von Neumann programming languages von Neumann regular ring von Neumann...

Regular ring, a ring such that all its localizations have Krull dimension equal to the minimal number of generators of the maximal ideal von Neumann regular...

John von Neumann (/vɒn ˈnɔɪmən/ von NOY-mən; Hungarian: Neumann János Lajos [ˈnɒjmɒn ˈjaːnoʃ ˈlɒjoʃ]; December 28, 1903 – February 8, 1957) was a Hungarian...

order-unit whose positive cone cannot be represented as V(R), for a von Neumann regular ring R. The given examples can have any cardinality greater than or...

Baer rings, Baer *-rings, Rickart rings, Rickart *-rings, and AW*-algebras are various attempts to give an algebraic analogue of von Neumann algebras...

token, in a von Neumann regular ring every finitely generated left and right ideal is a direct summand of R, and so von Neumann regular rings are left and...

xyx=x. Finally, regular ideal has been used to refer to an ideal J of a ring R such that the quotient ring R/J is von Neumann regular ring. This article...

that over a von Neumann regular ring, every submodule of every R-module is pure. This is because every module over a von Neumann regular ring is flat. The...

commutative von Neumann regular ring R, the same thing happens. Suppose a in R is not a zero divisor. Then in a von Neumann regular ring a = axa for some...

rings with multiplicative identity The Brown–McCoy radical is studied in much greater generality than associative rings with 1. A von Neumann regular...

finitely generated two-sided ideals of some (not necessarily unital) von Neumann regular ring (Wehrung 2000). (3) Conc L, for some sectionally complemented modular...

of a von Neumann regular ring. More precisely if the lattice has order n then the von Neumann regular ring can be taken to be an n by n matrix ring Mn(R)...

mathematics, strongly regular might refer to: Strongly regular graph Strongly regular ring, or "strongly von Neumann regular" ring This disambiguation page...

order at least 4 is isomorphic to the principal right ideals of a von Neumann regular ring. A projective space S can be defined abstractly as a set P (the...

First Course in Noncommutative Rings. Springer Science & Business Media. ISBN 978-1-4684-0406-7. Dedekind-infinite set Von Neumann regular ring v t e...

element Linear least squares (mathematics) Pseudo-determinant Von Neumann regular ring Ben-Israel & Greville 2003, p. 7 Campbell & Meyer 1991, p. 10 Nakamura...

endomorphism ring being a local ring. For a semisimple module, the endomorphism ring is a von Neumann regular ring. The endomorphism ring of a nonzero...

Every primitive ring is semiprimitive. The product of two fields is semiprimitive but not primitive. Every von Neumann regular ring is semiprimitive...

category of sets, every monomorphism f : A → A is an isomorphism. A von Neumann regular ring R has the analogous property in the category of (left or right)...

Generic flatness Flat morphism von Neumann regular ring – rings over which all modules are flat. Normally flat ring Proof: Suppose f : R → S {\displaystyle...

A / nil ⁡ ( A ) {\displaystyle A/\operatorname {nil} (A)} is a von Neumann regular ring, where nil ⁡ ( A ) {\displaystyle \operatorname {nil} (A)} is the...

left nor a right zero divisor In ring theory, a von Neumann regular element of a ring A regular element of a Lie algebra or Lie group This disambiguation...

and a ring has weak global dimension 0 if and only if it is a von Neumann regular ring. Let M be a graded module over a graded algebra, which is generated...

  von Neumann regular element : An element r of a ring R is von Neumann regular if there exists an element x of R such that r = rxr. 2.  A von Neumann regular...

semisimple ring is injective and projective. Since "projective" implies "flat", a semisimple ring is a von Neumann regular ring. Semisimple rings are of particular...

right (or every left) ideal is generated by an idempotent. A ring is von Neumann regular if and only if every finitely generated right (or every finitely...