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...

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...

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

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

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

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...

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

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...

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