Indecomposable

Indecomposable has multiple meanings in the field of mathematics:

  • indecomposable module, in algebra
  • indecomposable distribution, in probability
  • indecomposable continuum, in topology
  • indecomposability, in constructive mathematics

Other articles related to "indecomposable":

Additively Indecomposable Ordinal
... In set theory, a branch of mathematics, an additively indecomposable ordinal α is any ordinal number that is not 0 such that for any, we have The set of additively indecomposable ...
Structure Theorem For Finitely Generated Modules Over A Principal Ideal Domain - Generalizations - Indecomposable Modules
... By contrast, unique decomposition into indecomposable submodules does not generalize as far, and the failure is measured by the ideal class group, which ... both the module R and its submodule M generated by 2 and 1 + √−5 are indecomposable ... isomorphic to M, R ⊕ R is isomorphic to M ⊕ M thus the images of the M summands give indecomposable submodules L1, L2 < R ⊕ R which give a different decomposition of R ⊕ R ...
Indecomposable Module - Facts
... Every simple module is indecomposable ... ring of a module, one can tell whether the module is indecomposable if and only if the endomorphism ring does not contain an idempotent different from 0 and 1 ... direct sum of ker(f) and im(f).) A module of finite length is indecomposable if and only if its endomorphism ring is local ...
Principal Indecomposable Module - Definition
... A (left) principal indecomposable module of a ring R is a (left) submodule of R that is a direct summand of R and is an indecomposable module ... Alternatively, it is an indecomposable, projective, cyclic module ... Principal indecomposable modules are also called PIMs for short ...