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condition is stably finite. A trivial ring is stably finite but doesn't have IBN. Cohn, P. M. (December 6, 2012). "Basic Algebra: Groups, Rings and Fields"...

is not true for every ring R though. A ring R whose matrix rings all have the mentioned property is known as a stably finite ring (Lam 1999, p. 5). In...

mathematics, a stably free module is a module which is close to being free. A module M over a ring R is stably free if there exists a free finitely generated...

division ring (compare field of fractions in the commutative case). See also the Ore condition. Every nontrivial division ring or stably finite ring has invariant...

means of valuation rings. locally factorial The local rings are unique factorization domains. locally of finite presentation Cf. finite presentation above...

model takes into account the finite mass of the Adams ring, which is necessary to move the resonance closer to the ring. A byproduct of this hypothesis...

Equivalently, a ring is left-Noetherian (respectively right-Noetherian) if every left ideal (respectively right-ideal) is finitely generated. A ring is Noetherian...

and the drain. Thus, the output of every inverter in a ring oscillator changes within a finite amount of time after the input has changed. From here,...

{\widetilde {K}})\cong H_{n}(A_{*})} will be finitely generated if and only if these modules are stably-free. Stably-free modules vanish in reduced K-theory...

§ Stable properties, below. If the ring R is Noetherian, or, at least coherent, and if M is finitely generated, then the syzygy module is also finitely...

theory, a stable group is a group that is stable in the sense of stability theory. An important class of examples is provided by groups of finite Morley...

branch of mathematics. The theorem relates the Burnside ring of a finite group G to the stable cohomotopy of the classifying space BG. The conjecture was...

Finite-difference time-domain (FDTD) or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis...

ring S (often a field) is a ring (or sometimes an integral domain) that is finitely generated over S. algebraic-geometrical local ring A local ring that...

series can be used instead of finite sums. For example, the matrices whose column sums are convergent sequences form a ring. Analogously, the matrices whose...

Witt ring of C, and indeed any algebraically closed field or quadratically closed field, is Z/2Z. The Witt ring of R is Z. The Witt ring of a finite field...

distributive lattices states that the elements of any finite distributive lattice can be represented as finite sets, in such a way that the lattice operations...

in which differential rings, differential fields, and differential algebras are rings, fields, and algebras equipped with finitely many derivations. A natural...

prime ideals in the polynomial ring k [ X 1 , … , X n ] {\displaystyle k[X_{1},\dots ,X_{n}]} . Since such ideals are finitely generated, there are only |...

to Lam (1978) (§I.4, p. 26), a ring is right Hermite if any finitely generated stably free right module over the ring is free. This is equivalent to requiring...