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 ⊃...

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...

Neumann's no hidden variables proof von Neumann ordinal von Neumann paradox von Neumann probe von Neumann programming languages von Neumann regular ring...

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

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...

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

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...

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

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

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...

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...

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...

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

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...

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...

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...

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...

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

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...

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

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

respond to subsequent calls for service Goodearl, K. R. (1991), von Neumann regular rings (2 ed.), Malabar, FL: Robert E. Krieger Publishing Co. Inc., pp...

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)...

ring is said to be a Dedekind-finite ring (also called directly finite rings and Von Neumann finite rings) if ab = 1 implies ba = 1 for any two ring elements...

  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...

vector space over a division ring D. It is known that R is a left full linear ring if and only if R is von Neumann regular, left self-injective with socle...

Furthermore, as all elements are idempotents, Boolean rings are commutative von Neumann regular rings and hence absolutely flat, which means that every module...