structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian...

by the structure theorem, taking Z as the principal ideal domain. Finitely generated (say left) modules over a division ring are precisely finite dimensional...

fundamental theorem of finite abelian groups. The theorem, in both forms, in turn generalizes to the structure theorem for finitely generated modules over a principal...

words, a K[x]-module is a K-vector space M combined with a linear map from M to M. Applying the structure theorem for finitely generated modules over a principal...

principal ideal domain. The key result is the structure theorem: If R is a principal ideal domain, and M is a finitely generated R-module, then M {\displaystyle...

form of the structure theorem for finitely generated modules over a principal ideal domain, and for the special case of polynomial rings over a field, it...

the structure theorem for finitely generated modules over a principal ideal domain. In the case of finitely generated abelian groups, this theorem guarantees...

ideal domain and M is a finitely generated R-module. Then the structure theorem for finitely generated modules over a principal ideal domain gives a detailed...

element. Finitely generated ideal: This type of ideal is finitely generated as a module. Primitive ideal: A left primitive ideal is the annihilator of a simple...

useful structure theorem for finitely generated modules over a principal ideal domain (PID), it is natural to ask for a corresponding theory for finitely generated...

the structure theorem for finitely generated modules over a principal ideal domain, which includes the fundamental theorem of finitely generated abelian...

P} is finite is a straightforward application of the structure theorem for finitely generated modules over a principal ideal domain. For modules indexed...

= K[T], as in the structure theorem for finitely generated modules over a principal ideal domain. Then the spectrum of K[T] (as a ring) equals the spectrum...

Structure theorem may refer to: Structured program theorem, a result in programming language theory Structure theorem for finitely generated modules over...

theorems Composition series Length of a module Structure theorem for finitely generated modules over a principal ideal domain Homological dimension Projective...

finitely generated modules over a principal ideal domain. The theorem may be illustrated by the following application to linear algebra. Let V be a finite-dimensional...

infinite. Finitely-generated modules over principal ideal domains (PIDs) are classified by the structure theorem for finitely generated modules over a principal...

free A stably free module structure theorem The structure theorem for finitely generated modules over a principal ideal domain says that a finitely generated...

a module over a principal ideal domain (PID) occur in one form of the structure theorem for finitely generated modules over a principal ideal domain....

finitely generated modules over a principal ideal domain (abstract algebra) Structure theorem for Gaussian measures (measure theory) Structured program...

⊃ integral domains ⊃ integrally closed domains ⊃ GCD domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields ⊃...

operator on a finite-dimensional vector space. Specifically, applying the structure theorem for finitely generated modules over a principal ideal domain to this...

The structure theorem for finitely generated modules over a principal ideal domain applies to K[X], when K is a field. This means that every finitely generated...

theorem for finitely generated modules over a principal ideal domain to V, viewing it as an F[X]-module. The structure theorem provides a decomposition...

Rank–nullity theorem – In linear algebra, relation between 3 dimensions (by rank and nullity) Structure theorem for finitely generated modules over a principal ideal...

direct sum decomposition – see Structure theorem for finitely generated modules over a principal ideal domain § Uniqueness for example. Some authors distinguish...

application to the ring K[x] of the structure theorem for finitely generated modules over a principal ideal domain, of which it is a corollary. One can see that...

structure theorem is the standard structure theorem for finitely generated modules over a principal ideal domain. However, this argument fails if the indexing...

based upon a homotopical theory of modules over highly structured ring spectra. The homotopy category of such modules closely resembles the derived category...

a module over a principal ideal domain (PID) occur in one form of the structure theorem for finitely generated modules over a principal ideal domain....