In the mathematical field of ring theory, a ring R has the invariant basis number (IBN) property if all finitely generated free modules over R have a well-defined...

has invariant basis number, then by definition any two bases have the same cardinality. For example, nonzero commutative rings have invariant basis number...

ring does not satisfy the invariant basis number condition, unlike vector spaces, which always have a (possibly infinite) basis whose cardinality is then...

theorem can be generalized to arbitrary R-modules for rings R having invariant basis number. In the finitely generated case the proof uses only elementary arguments...

endomorphism are invariant under a change of basis. In other words, the spectrum of a matrix is invariant under a change of basis. The principal invariants of tensors...

integral basis for K {\displaystyle K} . The discriminant of K {\displaystyle K} is defined as det(t). It is an integer, and is an invariant property...

IBN in BBS software ICICI Bank (NYSE: IBN), bank based in India Invariant basis number, in mathematical ring theory Internet background noise This disambiguation...

In geometry, the Dehn invariant is a value used to determine whether one polyhedron can be cut into pieces and reassembled ("dissected") into another...

nonzero commutative ring with no zero divisors except 0. invariant A ring R has invariant basis number if Rm isomorphic to Rn as R-modules implies m = n. irreducible...

Hilbert in 1890 in his seminal article on invariant theory, where he solved several problems on invariants. In this article, he proved also two other...

In mathematics, the Arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by Turkish mathematician Cahit Arf (1941)...

presentation of a module. Countably generated module Flat module Invariant basis number "ac.commutative algebra – Existence of a minimal generating set...

which are not Morita invariant include commutative, local, reduced, domain, right (or left) Goldie, Frobenius, invariant basis number, and Dedekind finite...

addition to every stably free (left) module being free, it has invariant basis number. All commutative rings which are Hermite in the sense of Kaplansky...

basis allows many important properties of the ideal and the associated algebraic variety to be deduced easily, such as the dimension and the number of...

mathematical field of knot theory, the Arf invariant of a knot, named after Cahit Arf, is a knot invariant obtained from a quadratic form associated to...

goals of invariant theory was to solve the "finite basis problem". The sum or product of any two invariants is invariant, and the finite basis problem...

signals of "10 invariant and almost invariant glycines" as well as signals of hypervariable regions. Kabat produced the first numbering scheme in 1970...

closely related concept is self-similarity, where a function or curve is invariant under a discrete subset of the dilations. It is also possible for the...

in invariant theory, stating that the ring of invariants of a reductive group is finitely generated Hilbert's irreducibility theorem, in number theory...

BA = 1. This is a stronger property for a ring than having the invariant basis number (IBN) property. Namely, any nontrivial stably finite ring has IBN...

modules over local rings are free, and because local rings have invariant basis number, it follows that a local, right hereditary ring is a right fir,...

in the late 19th century forms the basis of modern group representation theory. In the nineteenth century, number systems called quaternions, tessarines...

matter physics. It indicates the mathematical group for the topological invariant of the topological insulators and topological superconductors, given a...

}=\gamma ^{0}\gamma ^{\mu }\gamma ^{0}.} The hermiticity conditions are not invariant under the action γ μ → S ( Λ ) γ μ S ( Λ ) − 1 {\displaystyle \gamma ^{\mu...

of the purity of number theory was shattered in the 1970s, when it was publicly announced that prime numbers could be used as the basis for the creation...

_{i=1}^{l}Y_{i}} where l is the number of distinct eigenvalues of A. Intuitively, we glob together the Jordan block invariant subspaces corresponding to the...

dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field. It is sometimes called Hamel dimension...

also change signs under reflections. Invariant (physics) Relative scalar Scalar (mathematics) "Details for IEV number 102-02-19: "scalar quantity"". IEC...

symmetric homogeneous polynomials in the basis elements e a {\displaystyle e_{a}} of the Lie algebra. The Casimir invariants are the irreducible homogeneous polynomials...